Name:_____________________
Hypothesis Testing
Directions: Complete each of the following problems. You must show work to
receive credit.
1. BFHS claims that their average ACT score is 23. A sample of 40 students has an average
ACT score of 21.
a. Determine the null hypothesis
b. Determine the alternative hypothesis
c. Calculate the test statistic
d. Calculate the p—value
e. Using 𝛼 = 0.01, do you “reject” or “fail to reject” the null hypothesis?
f. What does this mean in terms of your problem?
2. Data Analytics claims that the average Ph.D. holder in Idaho makes at least $75,000 per
year. A sample of 50 people with Ph.D. degrees have an average salary of $74,500.
a. Determine the null hypothesis
b. Determine the alternative hypothesis
c. Calculate the test statistic
d. Calculate the p—value
e. Using 𝛼 = 0.10, do you “reject” or “fail to reject” the null hypothesis?
f. What does this mean in terms of your problem?
3. Politico claims that 60% of men vote Republican. A survey of 7500 men shows that 4000
voted Republican.
a. Determine the null hypothesis
b. Determine the alternative hypothesis
c. Calculate the test statistic
d. Calculate the p—value
e. Using 𝛼 = 0.05, do you “reject” or “fail to reject” the null hypothesis?
f. What does this mean in terms of your original problem?
4. Brad claims that the average height of women from North Idaho is at least 66 inches. A
survey of 100 women from North Idaho have an average height of 65 inches.
a. Determine the null hypothesis
b. Determine the alternative hypothesis
c. Calculate the test statistic
d. Calculate the p—value
e. Using 𝛼 = 0.05, do you “reject” or “fail to reject” the null
hypothesis?
f. What does this mean in the context of your problem?
5. Herbert claims that the average tree on his property holds 250 board feet
of lumber. A survey of 20 trees have an average of 270 board feet of
lumber.
a. What is the null hypothesis?
b. What is the alternative hypothesis?
c. Calculate the value of the test statistic
d. Calculate the p—value
e. Using 𝛼 = 0.05, do you “reject” or “fail to reject” the null
hypothesis?
f. What does this mean in the context of your problem?
6. Eliza says that she can clap 100 times per minute. A test shows that she
clapped 475 times in five minutes.
a. What is the null hypothesis?
b. What is the alternative hypothesis?
c. Calculate the value of the test statistic
d. Calculate the p—value
e. Using 𝛼 = 0.05, do you “reject” or “fail to reject” the null
hypothesis?
f. What does this mean in the context of your problem?
7. Herb claims that everyone he knows has at least 5 siblings. A random
sample of 20 people Herb knows show an average of 4.2 siblings.
a. What is the null hypothesis?
b. What is the alternative hypothesis?
c. Calculate the value of the test statistic
d. Calculate the p—value
e. Using 𝛼 = 0.05, do you “reject” or “fail to reject” the null
hypothesis?
f. What does this mean in the context of your problem?
8. Bolt claims that he can run 100 meters in no more than 10.0 seconds. A
collection of 15 100 meter races show an average of 10.2 seconds.
a. What is the null hypothesis?
b. What is the alternative hypothesis?
c. Calculate the value of the test statistic
d. Calculate the p—value
e. Using 𝛼 = 0.05, do you “reject” or “fail to reject” the null
hypothesis?
f. What does this mean in the context of your problem?
9. Sunny claims that her happiness causes 100 people to smile per day. A
survey of one week shows that Sunny causes 108 people to smile per day
on average.
a. What is the null hypothesis?
b. What is the alternative hypothesis?
c. Calculate the value of the test statistic
d. Calculate the p—value
e. Using 𝛼 = 0.05, do you “reject” or “fail to reject” the null
hypothesis?
f. What does this mean in the context of your problem?
10.Newman claims that he can make at least $1000 per month by driving his
recycling to Michigan. A survey of 10 months shows that he made $950 per
month on average.
a. What is the null hypothesis?
b. What is the alternative hypothesis?
c. Calculate the value of the test statistic
d. Calculate the p—value
e. Using 𝛼 = 0.05, do you “reject” or “fail to reject” the null
hypothesis?
f. What does this mean in the context of your problem?