# Statistics - Hypothesis Testing

1. The General Social Survey is an annual survey given to about 1,500 U.S. adults selected at random. Each year, the survey contains several questions meant to probe respondents' views of employment. A recent survey contained the question "How important to your life is having a fulfilling job?" Of the 261 college graduates surveyed, 107 chose the response "Very important." Of the 121 people surveyed whose highest level of education was high school or less, 34 chose the response "Very important." Based on these data, can we conclude, at the 0.05 level of significance, that there is a difference between the proportion p1 of all U.S. college graduates who would answer "Very important" and the proportion p2 of all U.S. adults whose highest level of education was high school or less who would answer "Very important"?

Perform a two-tailed test. Then answer the 6 questions below.

Carry your intermediate computations to at least three decimal places and round your answers the same way.

1) The null hypothesis

2) The alternative hypothesis

3) The type of test statistic (Z, t, chi-square, etc)

4) The value of the test statistic

5) The p-value

6) (YES OR NO) Can we conclude that there is a difference between the two populations in the proportions who would answer "very important"?

2. The university data center has two main computers. The center wants to examine whether computer 1 is receiving tasks which require comparable processing time to those of computer 2. A random sample of 8 processing times from computer 1 showed a mean of 34 seconds with a standard deviation of 20 seconds, while a random sample of 14 processing times from computer 2 (chosen independently of those for computer 1) showed a mean of 52 seconds with a standard deviation of 17 seconds. Assume that the populations of processing times are normally distributed for each of the two computers, and that the variances are equal. Can we conclude, at the 0.05 level of significance, that the mean processing time of computer 1,p1 , is less than the mean processing time of computer 2, p2 ?

Perform a one-tailed test. Then answer the questions below.

Carry your intermediate computations to at least three decimal places and round your answers the same way.

1) The null hypothesis

2) The alternative hypothesis

3) The type of test statistic (Z, t, chi-square, etc)

4) The value of the test statistic

5) The p-value

6) (YES OR NO) Can we conclude that the mean processing time of computer 1 is less than the mean processing time of computer 2?

3. An industrial plant wants to determine which of two types of fuel, electric or gas, is more cost efficient (measured in cost per unit of energy). Independent random samples were taken of plants using electricity and plants using gas. These samples consisted of 11 plants using electricity, which had a mean cost per unit of $56.5 and standard deviation of $8.71, and 10 plants using gas, which had a mean of $58.4 and standard deviation of $8.75 . Assume that the populations of costs per unit are normally distributed for each type of fuel, and assume that the variances of these populations are equal. Can we conclude, at the 0.1 level of significance, that the mean cost per unit for plants using electricity, f1, differs from the mean cost per unit for plants using gas, f2 ?

Perform a two-tailed test. Then answer the 6 questions below.

Carry your intermediate computations to at least three decimal places and round your answers the same way.

1) The null hypothesis

2) The alternative hypothesis

3) The type of test statistic (Z, t, chi-square, etc)

4) The value of the test statistic

5) The two critical values at the 0.1 level of significance

6) (YES OR NO) Can we conclude that the mean cost per unit for plants using electricity differs from the mean cost per unit for plants using gas?

4. A presidential candidate's aide estimates that, among all college students, the proportion p who intend to vote in the upcoming election is at least 60%. If 119 out of a random sample of 205 college students expressed an intent to vote, can we reject the aide's estimate at the 0.05 level of significance?

Perform a one-tailed test and answer the questions below.

Carry your intermediate computations to at least three decimal places and round your answers to three as well.

1) The null hypothesis

2) The alternative hypothesis

3) The type of test statistic (ex. Z, t, Chi-Square, etc.)

4) The value of the test statistic

5) The critical value at the 0.05 level of significance

6) YES or NO. Can we reject the aide's estimate that the proportion of college students who intend to vote is at least 60%?

5. A decade-old study found that the proportion, p, of high school seniors who believed that "getting rich" was an important personal goal was 70%. A researcher decides to test whether or not that percentage still stands. He finds that, among the 205 high school seniors in his random sample, 147 believe that "getting rich" is an important goal. Can he conclude, at the 0.01 level of significance, that the proportion has indeed changed?

Perform a two-tailed test and answer the questions below.

Carry your intermediate computations to at least three decimal places and round your answers to three as well

1) The null hypothesis

2) The alternative hypothesis

3) The type of test statistic (ex. Z, t, Chi-Square, etc.)

4) The value of the test statistic

5) The p-value

6) YES or NO. Can we conclude that the proportion of high school seniors who believe that "getting rich" is an important goal has changed?

6. The historical reports from two major networks showed that the mean number of commercials aired during prime time was equal for both networks last year. In order to find out whether they still air the same number of commercials on average or not, random and independent samples of 50% recent prime time airings from both networks have been considered. The first network aired an average of 111.3 commercials during prime with a standard deviation of 4.4. The second network aired 108.7 commercials with a standard deviation of 4.8. Since the sample size is quite large, assume that the population standard deviations 4.4 and 4.8 can be estimated using the sample standard deviations. At the 0.01 level of significance, is there sufficient evidence to support the claim that the average number of commercials aired during prime time by the first station, S1 is not equal to the average number of commercials aired during prime time by the second station S2

Perform a two-tailed test and answer the questions below.

Carry your intermediate computations to at least three decimal places and round your answers to three as well.

1) The null hypothesis

2) The alternative hypothesis

3) The type of test statistic (ex. Z, t, Chi-Square, etc.)

4) The value of the test statistic

5) The two critical values at the 0.01 level of significance

6) YES or NO. Can we support the claim that the mean numer of commercials aired during prime time by the first network is not equal to the mean number of commercials aired during prime time by the second network?

[See the attached questions file.]

#### Solution Summary

Neat, step-by-step solutions are provided.