Date of submission: within 5 days of this post
A Simple random sample is a sample drawn in such a way that each member of ____________.
A)some chance of being selected in the sample.
B)an equal chance of being included in the sample.
C)a 1% chance of being included in the sample
Answer : B.
Sampling distribution is considered to be normal if distribution of the sample n is greater than:
A)20.
B)25.
C)30.
Answer : C.
Assume that a population has a mean of 14 with a standard deviation of 2. If a random sample of 49 observations is drawn from this population. The standard error of the sample mean is closest to:
A)0.04.
B)0.29.
C)2.00
Answer : B.
The population's mean is 30 and the mean of a sample of size 100 is 28.5. The variance of the sample is 25. The standard error of the sample mean is closest to:
A)0.05.
B)0.25.
C)0.50.
Answer : C.
A random sample of 100 computer store customers spent an average of $75 at the store. Assuming the distribution is normal and the population standard deviation is $20, the 95% confidence interval for the population mean is closest to:
A)$71.08 to $78.92.
B)$73.89 to $80.11.
C)$74.56 to $79.44.
Answer : A.
Best Computers, Inc., sells computers and computer parts by mail. A sample of 25 orders showed the mean time taken to ship out these orders was 70 hours with a sample standard deviation of 14 hours. Assuming the population is normally distributed, the 99% confidence interval for the population mean is:
A)70 ± 2.80 hours.
B)70 ± 6.98 hours.
C)70 ± 7.83 hours.
Answer : C.
A researcher claims that black horses are, on average, more than 30 lbs heavier than white horses, which average 1100 lbs. What is the null hypothesis?
A)Ho : µ < 1130 lbs
B)Ho : µ = 1130 lbs
C)Ho : µ = 1130 lbs
Answer : C.
A researcher claims that black horses are, on average, more than 30 lbs heavier than white horses, which average 1100 lbs. What is the alternative hypothesis?
A)Ha : µ > 1130 lbs
B)Ha : µ = 1130 lbs
C)Ha : µ = 1130 lbs
Answer : A.
If we were to test the hypothesis that college freshmen study 20 hours per week, we would express our null hypothesis as______________.
A)Ho : µ > 20 lbs
B)Ho : µ = 20 lbs
C)Ha : µ = 20 lbs
Answer : B.
If we were to test the hypothesis that college freshmen study 20 hours per week, we would express our alternative hypothesis as______________.
A)Ha : µ > 20 lbs
B)Ho : µ = 20 lbs
C)Ha : µ ≠ 20 lbs
Answer : C.
We have a medicine that is being manufactured and each pill is supposed to have 14 milligrams of the active ingredient. What are our null hypotheses?
A)Ho : µ > 14 lbs
B)Ho : µ = 14 lbs
C)Ho : µ = 14 lbs
Answer : B.
We have a medicine that is being manufactured and each pill is supposed to have 14 milligrams of the active ingredient. What are our alternative hypotheses?
A)Ho : µ > 14 lbs
B)Ho : µ = 14 lbs
C)Ha : µ ≠ 14 lbs
Answer : B.
We have a medicine that is being manufactured and each pill is supposed to have 14 milligrams of the active ingredient. ____tail test applied.
A)1
B)2
C)both a and b
Answer : B.
The school principal wants to test if it is true what teachers say that high school juniors use the computer an average 3.2 hours a day. What is our null hypotheses?
A)Ho : µ > 3.2 lbs
B)Ho : µ = 3.2 lbs
C)Ha : µ ≠ 3.2 lbs
Answer : B.
The school principal wants to test if it is true what teachers say that high school juniors use the computer an average 3.2 hours a day. What is our alternative hypotheses?
A)Ho : µ > 3.2 lbs
B)Ho : µ ≠ 3.2 lbs
C)Ha : µ ≠ 3.2 lbs
Answer : C.
We have a medicine that is being manufactured and each pill is supposed to have 14 milligrams of the active ingredient. ____tail test applied.
A)1
B)2
C)both a and b
Answer : B.
If the difference between the hypothesized population mean and the mean of the sample is large, we ___ the null hypothesis.
A)Accept
B)Reject
C)Do nothing
Answer : B.
If the difference between the hypothesized population mean and the mean of the sample is small, we ___ the null hypothesis.
A)Accept
B)Reject
C)Do nothing
Answer : A.
At the Chrysler manufacturing plant, there is a part that is supposed to weigh precisely 19 pounds. The engineers take a sample of parts and want to know if they meet the weight specifications. What is our null hypotheses?
A)Ho : µ = 19
B)Ho : µ ≠ 19
C)Ha : µ ≠ 19
Answer : A.
At the Chrysler manufacturing plant, there is a part that is supposed to weigh precisely 19 pounds. The engineers take a sample of parts and want to know if they meet the weight specifications. What is our alternative hypotheses?
A)Ho : µ = 19
B)Ho : µ ≠ 19
C)Ha : µ ≠ 19
Answer : B.
A researcher claims that black horses are, on average, more than 30 lbs heavier than white horses, which average 1100 lbs. What is the null hypothesis.
A)Ho : µ ≤ 1130
B)Ho : µ ≤ 1100
C)Ho : µ ≤ 1070
Answer : A.
A researcher claims that black horses are, on average, more than 30 lbs heavier than white horses, which average 1100 lbs. What is the alternative hypothesis.
A)Ha : µ > 1130
B)Ha : µ > 1100
C)Ha : µ ≤ 1070
Answer : A.
A researcher claims that black horses are, on average, more than 30 lbs heavier than white horses, which average 1100 lbs. What kind of test will be used.
A)right tail
B)left
C)none of above
Answer : A.
What is the critical value Zα/2 for a 95% confidence level, assuming a two-tailed test?
A)±1.98
B)±2.56
C)±1.96
Answer : C.
What would be the critical value for a right-tailed test with α = 0.01?
A)±1.98
B)±2.33
C)±1.96
Answer : B.
The school nurse thinks the average height of 7th graders has increased. The average height of a 7th grader five years ago was 145 cm with a standard deviation of 20 cm. She takes a random sample of 200 students and finds that the average height of her sample is 147 cm. Are 7th graders now taller than they were before? Conduct a single-tailed hypothesis test using a .05 significance level to evaluate the null and alternative hypotheses. value of Z-statistics would be___?
A)1.414
B)±2.33
C)±1.96
Answer : A.
The school nurse thinks the average height of 7th graders has increased. The average height of a 7th grader five years ago was 145 cm with a standard deviation of 20 cm. She takes a random sample of 200 students and finds that the average height of her sample is 147 cm. Are 7th graders now taller than they were before? Conduct a single-tailed hypothesis test using a .05 significance level to evaluate the null and alternative hypotheses. value of Z-statistics would be___?
A)1.414
B)±2.33
C)±1.96
Answer : A.
The school nurse thinks the average height of 7th graders has increased. The average height of a 7th grader five years ago was 145 cm with a standard deviation of 20 cm. She takes a random sample of 200 students and finds that the average height of her sample is 147 cm. Are 7th graders now taller than they were before? Conduct a single-tailed hypothesis test using a .05 significance level to evaluate the null and alternative hypotheses. value of Z-score(table value) would be___?
A)1.414
B)±1.64
C)±1.96
Answer : B.
The school nurse thinks the average height of 7th graders has increased. The average height of a 7th grader five years ago was 145 cm with a standard deviation of 20 cm. She takes a random sample of 200 students and finds that the average height of her sample is 147 cm. Are 7th graders now taller than they were before? Conduct a single-tailed hypothesis test using a .05 significance level to evaluate the null and alternative hypotheses. we will apply _____ test?
A)Z
B)t
C)none
Answer : A.
The school nurse thinks the average height of 7th graders has increased. The average height of a 7th grader five years ago was 145 cm with a standard deviation of 20 cm. She takes a random sample of 20 students and finds that the average height of her sample is 147 cm. Are 7th graders now taller than they were before? Conduct a single-tailed hypothesis test using a .05 significance level to evaluate the null and alternative hypotheses. we will apply _____ test?
A)Z
B)t
C)none
Answer : B.
A farmer is trying out a planting technique that he hopes will increase the yield on his pea plants. The average number of pods on one of his pea plants is 145 pods with a standard deviation of 100 pods. This year, after trying his new planting technique, he takes a random sample of his plants and finds the average number of pods to be 147. He wonders whether or not this is a statistically significant increase.What type of statistic will be applied?
A)Z
B)t
C)none
Answer : A.
if the Z-statistics is 0.24 and the Z-table value is 1.64. will you _______________ the hypothesis?
A)Accept
B)Reject
C)none
Answer : A.
A sample is a representative subset of a _______________.
A)population
B)parameter
C)sampling
Answer : A.
Suppose you had 40 samples of bags of candy, each of which contains some number of pieces. The number of pieces in each bag is said to be normally distributed. The mean number of candies in your sample is 38 pieces. The
standard deviation for bags in the population is 2 pieces. What is the average number of candies in each bag in the population? To answer this question, you need to create a confidence interval. Let’s assume that you have been
asked to report a confidence interval with 99% certainty.
A)37.18 to 38.82
B)38.82 to 37.18
C)37.18 to 39.82
Answer : A.
If we know the population mean & standard deviation. we can use ______ test.
A)Z
B)t
C)none
Answer : A.
If we do not know the population standard deviation but sample size is greater than 30. we can use ______ test.
A)Z
B)t
C)none
Answer : A.
If we do not know the population standard deviation but sample size is less than 30. we can use ______ test.
A)Z
B)t
C)none
Answer : B.
degree of freedom in test is equal to ____.
A)n
B)n-1
C)none
Answer : B.
A random sample of size 24 is taken from a normal population with a known standard deviation of 5 and the mean is 8. find the 99% confidence of interval for the population mean is?
A)5.62 to 10.38
B)6.62 to 10.38
C)none
Answer : A.
A random sample of size 24 is taken from a normal population with a known standard deviation of 5 and the mean is 8, 99% confidence of interval. what type of test will be applied?
A)Z
B)t
C)none
Answer : A.
A random sample of size 24 is taken from a normal population with a unknown standard deviation and the mean is 8, 99% confidence of interval. what type of test will be applied?
A)Z
B)t
C)none
Answer : B.
Statistical inference is the act of generalizing from the data (“sample”) to a larger phenomenon (“population”) with calculated degree of certainty.
A)True
B)False
C)none
Answer : A.
The two common forms of statistical inference are:Estimation and hypthesis.
A)True
B)False
C)none
Answer : A.
A random sample is drawn from a population of known standard deviation 11.3 . Construct a 90% confidence interval for the population mean based on the information given (not all of the information given need be used).
n=36,x¯=105.2,s=11.2
A)105.2 ± 3.10
B)107.2 ± 3.10
C)none
Answer : A.
A random sample is drawn from a population of known standard deviation 11.3 . Construct a 90% confidence interval for the population mean based on the information given (not all of the information given need be used).
n=100,x¯=105.2,s=11.2
A)105.2 ± 3.10
B)105.2 ± 1.86
C)none
Answer : B
A random sample is drawn from a population of known standard deviation 22.1 . Construct a 95% confidence interval for the population mean based on the information given (not all of the information given need be used).
n=121,x¯=82.4,s=21.9
A)17.1 ± 0.77
B)105.2 ± 1.86
C)none
Answer : A.
A random sample is drawn from a population of known standard deviation 22.1 . Construct a 95% confidence interval for the population mean based on the information given (not all of the information given need be used).
n=81,x¯=82.4,s=21.9
A)17.1 ± 0.77
B)17.1 ± 0.42
C)none
Answer : B.
A government agency was charged by the legislature with estimating the length of time it takes citizens to fill out various forms. Two hundred randomly selected adults were timed as they filled out a particular form. The times required had mean 12.8 minutes with standard deviation 1.7 minutes. Construct a 90% confidence interval for the mean time taken for all adults to fill out this form.
A)12.8 ± 0.20
B)105.2 ± 1.86
C)none
Answer : A.
On every passenger vehicle that it tests an automotive magazine measures, at true speed 55 mph, the difference between the true speed of the vehicle and the speed indicated by the speedometer. For 36 vehicles tested the mean difference was −1.2 mph with standard deviation 0.2 mph. Construct a 90% confidence interval for the mean difference between true speed and indicated speed for all vehicles.
A)12.8 ± 0.20
B)−1.2 ± 0.05
C)none
Answer : B.
A sample of 250 workers aged 16 and older produced an average length of time with the current employer (job tenure) of 4.4 years with standard deviation 3.8 years. Construct a 99.9% confidence interval for the mean job tenure of all workers aged 16 or older.
A)12.8 ± 0.20
B)4.4 ± 0.79
C)none
Answer : B.
Point estimate give a ______________ value/s.
A)single
B)Range of
C)none
Answer : A.
Interval estimate give a ______________ value/s.
A)single
B)Range of
C)none
Answer : B.
A range of values constructed from sample data so that the population parameter is likely to occur within that range at a specified probability. The specified probability is called
A)single
B)Range of
C)the level of confidence.
Answer : C.
Ninety-five percent of all confidence intervals computed from random samples selected from a population will contain the population mean. These intervals are computed
using a z-statistic equal to 1.96.
A)True
B)False
Answer : A.
Ninety percent of all confidence intervals computed from random samples selected from a population will contain the population mean. These confidence intervals are
computed using a z-statistic equal to 1.65.
A)True
B)False
Answer : A.
σx is the symbol for the standard error of the mean.
A)True
B)False
Answer : A.
σ is the sample standard deviation.
A)True
B)False
Answer : B.
n is the number of observations in the sample.
A)True
B)False
Answer : A.
µ represents population standard deviation.
A)True
B)False
Answer : B.
s represents population standard deviation.
A)True
B)False
Answer : A.
x represents population standard deviation.
A)True
B)False
Answer : B.
Sample is a subset of a population.
A)True
B)False
Answer : A.
In statistics population refers to no of citizens live in a country.
A)True
B)False
Answer : B.
In inferential statistics we draw the inference about the sample on the basis of population.
A)True
B)False
Answer : B.
Probability Basics
A bag contains 5 red balls and 3 green balls. What is the probability of drawing a red ball?
a) 1/8
b) 3/8
c) 5/8
d) 3/5
Answer: c) 5/8
What is the probability of getting an even number when a fair six-sided die is rolled?
a) 1/6
b) 1/3
c) 1/2
d) 2/3
Answer: c) 1/2
If two coins are flipped, what is the probability of getting two heads?
a) 1/4
b) 1/2
c) 3/4
d) 1/8
Answer: a) 1/4
Conditional Probability
Given that event A and event B are independent, if P(A) = 0.3 and P(B) = 0.5, what is P(A ∩ B)?
a) 0.15
b) 0.20
c) 0.25
d) 0.30
Answer: a) 0.15
In a deck of 52 cards, what is the probability of drawing a queen given that the card is a face card?
a) 1/13
b) 1/4
c) 1/3
d) 1/52
Answer: c) 1/3
Combinatorics and Probability
What is the probability of drawing an ace from a standard deck of 52 cards?
a) 1/52
b) 1/13
c) 1/4
d) 1/3
Answer: b) 1/13
How many ways can you choose 2 cards from a deck of 52 cards?
a) 1326
b) 2652
c) 2704
d) 1024
Answer: a) 1326
Binomial Probability
If a coin is flipped 4 times, what is the probability of getting exactly 2 heads?
a) 3/8
b) 1/4
c) 5/16
d) 6/16
Answer: a) 3/8
In a binomial experiment with n = 5 trials and probability of success p = 0.4, what is the probability of exactly 3 successes? (Use binomial probability formula)
a) 0.2304
b) 0.3456
c) 0.2765
d) 0.2896
Answer: a) 0.2304
Poisson Probability
If the average number of emails received per hour is 5, what is the probability of receiving exactly 3 emails in an hour? (Use Poisson formula)
a) 0.1404
b) 0.2337
c) 0.2835
d) 0.3523
Answer: b) 0.2337
Normal Distribution
If X is normally distributed with a mean of 100 and a standard deviation of 15, what is the probability that X is less than 110? (Use Z-table)
a) 0.7486
b) 0.8413
c) 0.9332
d) 0.9772
Answer: b) 0.8413
What is the probability that a standard normal variable is between -1 and 1?
a) 0.6826
b) 0.7514
c) 0.8413
d) 0.9213
Answer: a) 0.6826
Continuous Probability Distributions
If X is uniformly distributed between 0 and 10, what is the probability that X is between 3 and 7?
a) 0.2
b) 0.3
c) 0.4
d) 0.5
Answer: c) 0.4
Expected Value
If you roll a fair die, what is the expected value of the outcome?
a) 2.5
b) 3.5
c) 4.5
d) 5.5
Answer: b) 3.5
What is the expected value of the number of heads when a fair coin is flipped 10 times?
a) 4
b) 5
c) 6
d) 7
Answer: b) 5
Variance and Standard Deviation
What is the variance of the number of heads when a fair coin is flipped 10 times?
a) 2
b) 2.5
c) 3
d) 4
Answer: b) 2.5
If X is a random variable with a mean of 50 and a variance of 25, what is the standard deviation of X?
a) 4
b) 5
c) 6
d) 7
Answer: b) 5
Bayes' Theorem
If P(A) = 0.2, P(B) = 0.5, and P(A ∩ B) = 0.1, what is P(A|B)?
a) 0.1
b) 0.2
c) 0.3
d) 0.4
Answer: b) 0.2
If 1% of a population has a disease and a test for the disease has a 99% sensitivity and a 98% specificity, what is the probability that a person has the disease given that they tested positive? (Use Bayes' Theorem)
a) 0.332
b) 0.204
c) 0.337
d) 0.428
Answer: c) 0.337
Law of Total Probability
If a factory has 3 machines producing 30%, 40%, and 30% of the items, respectively, with defect rates of 1%, 2%, and 3%, what is the overall probability of an item being defective?
a) 0.020
b) 0.021
c) 0.022
d) 0.023
Answer: b) 0.021
Which of the following is an example of simple random sampling?
A. Selecting every 10th person from a list of names
B. Drawing names from a hat where each name has an equal chance of being selected
C. Dividing the population into strata and sampling from each stratum
D. Selecting a sample based on the researcher’s judgment
Answer: B
In stratified sampling, the population is divided into:
A. Clusters
B. Strata
C. Groups
D. Sections
Answer: B
Which sampling method involves selecting a random starting point and then selecting every nth element in the population?
A. Simple random sampling
B. Systematic sampling
C. Stratified sampling
D. Cluster sampling
Answer: B
What type of sampling involves dividing the population into groups and then randomly selecting entire groups?
A. Simple random sampling
B. Stratified sampling
C. Cluster sampling
D. Systematic sampling
Answer: C
Which type of sampling is best used when the population is heterogeneous and can be divided into homogeneous subgroups?
A. Simple random sampling
B. Stratified sampling
C. Cluster sampling
D. Convenience sampling
Answer: B
Convenience sampling is best described as:
A. Sampling based on ease of access
B. Sampling based on random selection
C. Sampling from predefined strata
D. Sampling using a systematic approach
Answer: A
What is the primary disadvantage of convenience sampling?
A. It is time-consuming
B. It may introduce significant bias
C. It requires complex statistical tools
D. It ensures equal representation
Answer: B
Which of the following is a non-probability sampling method?
A. Simple random sampling
B. Systematic sampling
C. Stratified sampling
D. Quota sampling
Answer: D
In which sampling method are participants selected based on specific characteristics or criteria?
A. Simple random sampling
B. Stratified sampling
C. Purposive (judgmental) sampling
D. Cluster sampling
Answer: C
Which type of sampling technique would be most appropriate for conducting a national survey where time and resources are limited?
A. Simple random sampling
B. Stratified sampling
C. Cluster sampling
D. Convenience sampling
Answer: C
Population is equal to 4, 6, 12, 10 without replacement and with a size of 2 calculate Ẋ = µ and mean of all sample mean is equal to population mean?
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