_____1. (10 pts) When conducting a hypothesis test, which one of the following p-values would you feel most confident to reject the null hypothesis?
a. 0.05
b. 0.01
c. 0.99
d. 0.005
e. 0.995
_____2. (10 pts) A weatherman stated a null hypothesis that during the month of September, the mean daily temperature of Boston was the same as the mean daily temperature of New York. His alternative hypothesis was that mean temperatures in these two cities were different. He computed a p-value of 0.275. Using a confidence level of 90%, he should conclude:
a. In September, Boston was colder than New York
b. In September, New York was colder than Boston
c. Reject the null hypothesis
d. Fail to reject the null hypothesis
e. None of the above.
_____3. (10 pts) A teacher assumed the average grade for a quiz was 4.5. A sample of 20 students took the test and the 95% confidence interval of the mean test grade was (4.75, 5.44). Based on this information, can we reject the teacher’s assumption?
a. Yes
b. No
c. Not enough information provided
_____4. (10 pts) Which of the following descriptions of confidence intervals is correct? (Select all that apply)
a. If a 99% confidence interval contains 0, then the 95% confidence interval contains 0
b. If a 95% confidence interval contains 0, then the 99% confidence interval contains 0
c. If a 99% confidence interval contains 1, then the 95% confidence interval contains 1
d. If a 95% confidence interval contains 1, then the 99% confidence interval contains 1
e. None of the above are correct about confidence intervals.
_____5. (10 pts) Imagine a researcher presented a null hypothesis that in a certain community, the average energy expenditure is 2,100 calories per day. He randomly sampled 100 people in that particular community. He computed a t value using a two-tailed test statistic and the associated p-value was 0.08. Given a 90% confidence level, he should conclude:
a. The average energy expenditure is greater than 2,100 calories per day
b. The average energy expenditure is less than 2,100 calories per day
c. The average energy expenditure is not equal to 2,100 calories per day
d. Fail to reject the null hypothesis
e. None of the above
_____6. (10 pts) A researcher wanted to test the effect of the new drug on reducing blood pressure. In the study, there were 50 participants. The researcher measured the participants’ blood pressure before and after the drug was administered. If we want to compare the mean blood pressure from the two time-periods with a two-tailed t test, how many degrees of freedom are there?
a. 100
b. 99
c. 98
d. 49
e. 48
_____7. (10 pts) In a statistical hypothesis test, how is the rejection region impacted when α, the level of significance, is increased?
a. The answer depends on the value of β
b. The size of the rejection region decreases
c. The size of the rejection region increases
d. The rejection region is unaltered
e. None of the above
8. _____ (15 points) The UMUC bookstore states the average textbook costs $75. A randomly selected sample of 16 new textbooks at the UMUC bookstore had a mean price of $82.54 and sample standard deviation of $15.50. Use a 0.05 significance level to test the claim that the mean price of textbooks at the UMUC bookstore is significantly more than $75 (use the p-value method). Show your work.
a. Give the symbolic null & alternative hypotheses. Use proper notation.
H0: ______________________ HA: ______________________
b. Determine the test statistic (round to 3 decimal places): __________________
c. Determine the p-value (round to 3 decimal places): __________________
d. Result (Circle one & justify): REJECT 𝑯𝟎 FAIL TO REJECT 𝑯𝟎
Reason: ______________________________________________________________________
e. State a conclusion within the context of the scenario:
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
9. (15 points) Researchers interviewed college students in the United States and Europe. The mean age of 81 United States college students was 21 with a standard deviation of 6. The mean age of 92 European college students was 19 with a standard deviation of 7. Is the mean age of college students in Europe lower than the mean age in the United States? Test at a 0.03 significance level. Use the value of 170.885 for the degrees of freedom. Show your work. HINT: See Illowsky, Chapter 10.
a. Give the symbolic null & alternative hypotheses. Use correct notation.
H0: ______________________ HA: ______________________
b. Determine the test statistic (round to 3 decimal places): __________________
c. Determine the p-value (round to 3 decimal places): __________________
d. Result (Circle one & justify): REJECT 𝑯𝟎 FAIL TO REJECT 𝑯𝟎
Reason: ______________________________________________________________________
e. State a conclusion within the context of the scenario:
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
