STAT 2023, Assignment 16, Some random exam questions, Lesson 15, t-hypothesis
tests estimated with Z tests, & Introduction to Lesson 16, Inferences on Proportions
Part One: Some random past exam questions –all of these questions can be found
on page two of past third exams.
1. A sample of 196 stocks in a personal portfolio had an average return of 8.2%
since the end of the fiscal year and a standard deviation of 1.4%. Based on this
sample of 196 stocks what is a 95% confidence interval to estimate the mean
return of the population of stocks from which this sample was drawn? State the
limits on your interval with three digits past the decimal.
2. Assume a 99% confidence interval to estimate the mean cost of a semester of
full-time college at Oklahoma State University is ($4,800, $5,600). What is the
numerical value of the point estimate for the mean cost of a semester of full-time
college at Oklahoma State University?
3. If the test statistic in a two tail z hypothesis test is –1.85, what is the p-value for
the test?
4. If the rejection rule for a right tail z test is to reject the null hypothesis if the test
statistic is more than the value 1.96, what is the significance level of the
hypothesis test?
5. What is the absolute value of the test statistic if the p-value in a two-tail
hypothesis test based on a large sample is equal to 0.1052? State a positive
value.
6. If the sum of the data values from a sample with 300 observations is 6,600, what
is the numerical value of the point estimate for the mean of the population from
which the sample was drawn?
7. If a researcher knows that the t-test statistic in a left tail hypothesis test based on
a sample of 20 observations is equal to the value -3.4, then the p-value of the
test would be less than what amount?
8. What is the p-value of a left-tail hypothesis test based on a large sample if the
test statistic value is -1.58?
9. If a 90% confidence interval to estimate a population mean is (54.7, 68.3) what is
the value of the point estimate for the population mean?
10. What is the value of the test statistic if the p-value in a left-tail hypothesis test
based on a large sample is equal to 0.0116?
11. If a 95% confidence interval based on a large sample to estimate a population
mean is (787.42, 838.38) then what is the value of the standard error of the point
estimate for the population mean?
12. If a random sample of 5 observations has been selected with value 4, 2, 2, 3, and
4. What is the numerical value of the point estimate for the population mean?
13. If a random sample of 5 observations has been selected with value 4, 2, 2, 3, and
4. What is the numerical value of the point estimate for the population variance?
14. How many observations are needed in order to produce a 95% confidence
interval to estimate the mean adult female coyote weight to within 0.75 pounds?
Assume the standard deviation of the weights for adult female coyotes is 2.2
pounds.
15. What is the critical value or rejection point associated with a 10% alpha value in a
right-tail hypothesis test based on a sample with 10 observations?
Part Two: Estimating t-tests with Z tests
An advertiser on the web is interested in estimating the mean number of links that a
customer would use from a certain web site. Assume that a random sample of 676
customer visits to a certain web site was examined. The number of links used from the
web site for these 676 customers is equal to 4.8 links with a standard deviation of 2.6
links. Use this information to answer the questions below.
16. What is the point estimate for the mean number of links used from the web site?
17. What is the estimated standard error for the point estimate for the mean number
of links used from the web site?
18. Assume that the estimated standard error of the point estimate for the mean
number of links used from the web site is 0.12. What is the numerical value of
the bound of error for a 95% confidence interval to estimate the mean number of
links used from the web site? State four digits past the decimal.
19. If the estimated standard error for the point estimate for the mean number of links
used from the web site is 0.12 what is the numerical value of the test statistic to
test whether the mean number of links used from the web site is 5.1 links?
20. Assume the test statistic value is -2.5 and that the research question is, “Do the
data provide evidence that the mean number of links used from the website
differs from 5.1?” What is the resulting p-value in the hypothesis test if the tdistribution with 675 degree of freedom is estimated with a Z distribution?
21. Assume the resulting p-value is 0.012. Complete the following sentences.
22. If the null hypothesis that the mean number of links used from this website is
equal to 5.1 is rejected, then the chance of error in that case is __________ .
23. If you decide to reject Ho based on these data then the chance you are wrong
is __________.
24. At the 1% significance level the null hypothesis _______________ (would or
would not?) be rejected since the p-value of the test is 0.012 which exceeds
_________ .
25. At the 5% significance level the null hypothesis _______________ (would or
would not?) be rejected since the p-value of the test is 0.012 which is less
than ___________ .
Part Three: Reading and Studying
26. Read and Study Lesson 16. Write four sentence summary of Lesson 16 in your
own words.