WorksheetsInference for Means and Proportions Review
Total questions: 16
Worksheet time: 33mins
Which of the following is not a condition that needs to be checked for inference for proportions?
Ensuring that the sample is independent
Making sure the sample is representative of the population
n*p0 > 10, n*q0 > 10
n*p-hat > 10, n*q-hat > 10
Your conclusion about a hypothesis test should have all of the following characteristics EXCEPT
stating your conclusion in reference to the alternative hypothesis
a comparison of your p-value to a specific alpha-level
a clear link to the context of the problem
a confidence interval to further show that your conclusion is correct
z* is the critical value for which of the following tests/intervals?
I. 1-prop. z-test
II. 2-prop. z-interval
III. 1-sample t-test
IV. 2-sample t-interval
I only
I and II only
I, II, and III only
All of the above
III and IV only
Which calculator function allows you to find the test statistic for a 2-proportion z-interval?
normalcdf
invNorm
tcdf
invT
What is the critical value for a 95% confidence interval for proportions?
z = 1.645
z = 1.96
z = -1.645
z = -1.96
84% of Russians believe that the Sochi Olympics promoted sports development in Russia. The poll of 2,000 people had a margin of error of 2%. What is the best description of what this 2% M.E. means?
Not all of the 2,000 adults knew something about the Olympics
About 2% of the 2,000 adults polled refused to answer
About 2% of adults were expected to change their minds between the time of the poll and its publication time
The difference between the sample percentage and the population percentage is likely to be less than 2%
There is a 2% chance that this survey captured the true proportion of Russian adult citizens who would answer yes to the question.
A rubber band man claims that p, the proportion of bands that snap when stretched beyond 8 inches, is no more than 0.03. Some customers have complained that this happens more frequently. Which of the following sets of hypotheses would the customers used to conduct an experiment to test the rubber band man's claim?
H0: p ≠ 0.03, HA: p = 0.03
H0: p = 0.03, HA: p > 0.03
H0: p = 0.03, HA: p ≠ 0.03
H0: p = 0.03, HA: p < 0.03
H0: p > 0.03, HA: p = 0.03
There is a law in ND saying that the ratio of elementary students to teachers can be no more than 22:1. A hypothesis test is performed to determine if the proportion of schools is above 25% using an SRS of 85 schools. At the 0.05 significance level, what conclusion can be made if 32 of the schools surveyed exceed this ratio?
Since the p-value is less than the level of significance level, the null hypothesis should be rejected. There is significant evidence that the true proportion of schools with a higher ratio of more than 25%.
Since the p-value is greater than the level of significance level, the null hypothesis should be rejected. There is significant evidence that the true proportion of schools with a higher ratio of more than 25%.
Since the p-value is less than the level of significance level, the null hypothesis should not be rejected. There is not significant evidence that the true proportion of schools with a higher ratio of more than 25%.
Since p-hat = 0.376 > 0.05, the null hypothesis should not be rejected. There is not significant evidence that the true proportion of schools with a higher ratio is greater than 25%.
Since p-hat = 0.376 > 0.05, the null hypothesis should be rejected. There is significant evidence that the true proportion of schools with a higher ratio is greater than 25%.
900 men who practice yoga are surveyed to determine if they report low stress levels. The CFO of the surveying company is concerned about the costs associated with surveying 900 men, so she suggests sampling 100 men. Assuming the sample proportion does not change, what effect on the width of the confidence interval would occur in they were to survey 100 men instead of 900?
The width of the interval based on 100 men would be about 9 times wider than the interval with 900 men.
The width of the interval based on 100 men would be about 3 times wider than the interval with 900 men.
The width of the interval based on 100 men would be about the same as the interval with 900 men.
The width of the interval based on 100 men would be about 1/3 the width of the interval with 900 men.
The width of the interval based on 100 men would be about 1/9 the width of the interval with 900 men.
In a random of 850 city high school students, 768 said they had access to the internet during school hours. 308 of 355 rural high school students said they had access. which of the following is the p-value for a significance test to determine if these data provide evidence that the proportion of high school students in city areas who have internet access is different than those who go to rural schools?
0.002
0.011
0.022
0.033
0.066
Jimmy is interested in comparing the fitness level of the members of his gym to the levels at a competing gym. He randomly selected 125 members of his gym and found 75 passed a fitness test. 70 of 95 at the other gym passed. Which interval estimates, with 96% confidence, the difference in proportion of members in Jimmy's gym who can pass the test and the proportion from the other gym who can pass?
(-0.2404, -0.033)
(-0.2602, -0.0135)
(-0.2661, -0.0076)
(-0.3490, -0.1099)
(-0.3547, -0.1042)
A restaurant manager will randomly select a sample of filled cups each day and measure the volume of liquid in each cup. Past measurements have shown that the standard deviation of liquid dispensed by this machine is 0.2 ounces. An estimate of the mean volume must be reported within a margin of error of 0.1 ounces with 98% confidence. What is the minimum sample size for the number of drinks the manager must select?
2
5
16
17
22
A nutritionist claims U.S. children drink an average of less than 2 glasses of milk per day. Based on an SRS of 30 children, the p-value of H0: μ = 2 vs. HA: μ < 2 is 0.0015. What is the correct interpretation of the p-value?
The probability that she fails to reject the null hypothesis is 0.015%
The probability that she rejects the null is 0.015%
She can be 99.85% confident that the alternative hypothesis is true
About 0.15% of all samples would product a test statistics at least as extreme as ours if the null hypothesis is true.
About 99.85% of all samples would product a test statistics at least as extreme as ours if the null hypothesis is true.
The process of making cough drops yields drops with varying amounts of the active ingredient. It is claimed that the average amount of this ingredient per tablet is at least 400mg. We test a random sample of 90 tablets. The mean content of the active ingredient for the sample is 396.8mg, while the standard deviation is 31mg. What is the approximate p-value for the appropriate test?
0.050
0.100
0.165
0.330
0.335
A major department store wants to compare the mean number of customers an employee can process per hour using two new scanning systems. 100 employees are randomly selected and then randomly assigned to one of the new systems. After each group of 50 has been trained on one scanning system and 50 on the other, the number of customers processed per hour is recorded. Which test is most appropriate for this situation?
1-sample t-test
2-sample t-test
Paired t-test
1-sample z-test
2-sample z-test
Which of the following statements is/are true about a t-distribution with k degrees of freedom?
I. A t-distribution has a larger variance than the standard normal distribution.
II. As the number of degrees of freedom increases, the t-distribution approaches a standard normal distribution.
III. A t-statistics of 3.5 or higher with k degrees of freedom is more likely that a t-statistic of 3.5 or higher with k+1 degrees of freedom.
I only
II only
I and II only
II and III only
I, II, and III
