# Testing of hypothesis problems

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II Solve each problem below. Be sure to show essential calculations.

11. The following statements refer to the alternate hypothesis. In the space provided, in symbolic form using H0, and H1 , write the null and alternate hypothesis.

a. The mean pulse of lawyers is different from 90 beats per minute.

H0: __________________________________________________________________

H1: __________________________________________________________________

b. The mean salary of college presidents is less than $162,500.

H0: __________________________________________________________________

H1: __________________________________________________________________

c. The mean IQ score of 20 year olds is more than 100.

H0: __________________________________________________________________

H1: __________________________________________________________________

d. The mean annual income of sales associates is less than $32,000.

H0: __________________________________________________________________

H1: __________________________________________________________________

12. A recent article in a computer magazine suggested that the mean time to fully learn a new software program is 40 hours. A sample of 100 first-time users of a new statistics program revealed the mean time to learn it was 39 hours with the standard deviation of 8 hours. At the 0.05 significance level, can we conclude that users learn the package in less than a mean of 40 hours?

µ (population mean): _______

s (population standard deviation): _______

X (sample mean): _______

s (sample standard deviation): _______

a (significance level): _______

p (population proportion): _______

p (sample proportion): _______

a. State the null and alternate hypotheses.

H0: __________________

H1: __________________

b. Find the critical value

c. State the decision rule.

d. Compute the value of the test statistic.

e. Find the p-value

f. What is your decision regarding the null hypothesis? Interpret the result.

13. A vinyl siding company claims that the mean time to install siding on a medium-size house is at most 20 hours with a standard deviation of 3.7 hours. A random sample of 40 houses sided in the last three years has a mean installation time of 20.8 hours. At the 0.05 significance level, can a claim be made that it takes longer on average than 20 hours to side a house?

µ (population mean): _______

s (population standard deviation): _______

X (sample mean): _______

s (sample standard deviation): _______

a (significance level): _______

p (population proportion): _______

p (sample proportion): _______

a. State the null and alternate hypotheses.

H0: __________________

H1: __________________

b. Find the critical value

c. State the decision rule.

d. Compute the value of the test statistic.

e. Find the p-value

f. What is your decision regarding the null hypothesis? Interpret the result.

14. The mean cleanup and redecorating time for a one-bedroom student apartment at campus Housing is 16 hours. The time for the cleanup and redecorating process follows the normal distribution. The campus Housing administration instituted a "fee and fine system" that encourages students to clean their apartments when they vacate them. This should shorten the cleanup and redecorating time. A sample of 15 apartments had a mean cleanup and redecorating time of 14.5 hours with a standard deviation of 1.5 hours. Does use of the "fee and fine system" decrease the cleanup and redecorating time? Follow the five-step hypothesis testing procedure using the 0.05 significance level.

µ (population mean): _______

s (population standard deviation): _______

X (sample mean): _______

s (sample standard deviation): _______

a (significance level): _______

p (population proportion): _______

p (sample proportion): _______

a. State the null and alternate hypotheses.

H0: __________________

H1: __________________

b. Find the critical value

c. State the decision rule.

d. Compute the value of the test statistic.

e. Find the p-value

f. What is your decision regarding the null hypothesis? Interpret the result.

15. A typical college student drinks an average of 96 ounces per day of various beverages that contain caffeine. A sample of 12 students at Wallace College revealed the following amounts of beverages consumed containing caffeine:

108 96 84 84 120 96 108 132 72 120 72 96

Can we conclude that the average amount of beverages consumed containing caffeine at Ownes College is the same as the typical college student? Use the hypothesis testing procedure.

µ (population mean): _______

s (population standard deviation): _______

X (sample mean): _______

s (sample standard deviation): _______

a (significance level): _______

p (population proportion): _______

p (sample proportion): _______

a. State the null and alternate hypotheses.

H0: __________________

H1: __________________

b. Find the critical value

c. State the decision rule.

d. Compute the value of the test statistic.

e. Find the p-value

f. What is your decision regarding the null hypothesis? Interpret the result.

16. CherryBerry Soda, Inc. claims that 15 percent of the population can identify its products. In efforts to boost their identity, CherryBerry employs a famous spokesperson to advertise. A survey is then taken to assess the results of the ad campaign. The results show that 17 percent of the 1000 respondents can identify CherryBerry products. Has the advertising campaign increased product identity or is the difference due to chance? Use the 0.10 significance level.

µ (population mean): _______

s (population standard deviation): _______

X (sample mean): _______

s (sample standard deviation): _______

a (significance level): _______

p (population proportion): _______

p (sample proportion): _______

a. State the null and alternate hypotheses.

H0: __________________

H1: __________________

b. Find the critical value

c. State the decision rule.

d. Compute the value of the test statistic.

e. Find the p-value

f. What is your decision regarding the null hypothesis? Interpret the result.

17. Traditionally, two percent of the citizens of the United States live in a foreign country because they are disenchanted with U.S. politics or social attitudes. In order to test if this proportion has increased since the September 11, 2001, terror attacks, U.S. consulates contacted a random sample of 400 of these expatriates. The sample yields 12 people who report they are living overseas because of political or social attitudes. Can you conclude this data shows the proportion of politically motivated expatriates has increased? Use the 0.05 significance level.

µ (population mean): _______

s (population standard deviation): _______

X (sample mean): _______

s (sample standard deviation): _______

a (significance level): _______

p (population proportion): _______

p (sample proportion): _______

a. State the null and alternate hypotheses.

H0: __________________

H1: __________________

b. Find the critical value

c. State the decision rule.

d. Compute the value of the test statistic.

e. Find the p-value

f. What is your decision regarding the null hypothesis? Inter

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