Exam 9: Hypothesis Testing

At one school, the average amount of time that tenth-graders spend watching television each week is 21.6 hours. The principal introduces a campaign to encourage the students to watch less television. One year later, the principal wants to perform a hypothesis test to determine whether the average Amount of time spent watching television per week has decreased. The hypotheses are: :\mu=21.6 hours :\mu<21.6 hours Explain the meaning of a correct decision.

A two-tailed test is conducted at the 0.10 significance level. What is the P-value required to reject the null hypothesis?

A long-distance telephone company claims that the mean duration of long-distance telephone calls originating in one town was not equal to 9.4 minutes, which is the average for the state. Determine The null and alternative hypotheses for the test described.

The owner of a football team claims that the mean attendance at games is greater than 83,900. State the null hypothesis and the alternative hypothesis for a test of significance.

In 1990, the average duration of long-distance telephone calls originating in one town was 9.4 minutes. A long-distance telephone company wants to perform a hypothesis test to determine whether the average duration of long-distance phone calls has changed from the 1990 mean of 9.4 minutes. The hypotheses are: :\mu=9.4 minutes :\mu9.4 minutes Explain the meaning of a correct decision.

A researcher claims that the amounts of acetaminophen in a certain brand of cold tablets have a mean different from the 600 mg claimed by the manufacturer. Test this claim at the 0.02 level of significance. The mean acetaminophen content for a random sample of n = 41 tablets is 603.3 mg. Assume that the population standard deviation is 4.9 mg.

In 1990, the average math SAT score for students at one school was 510. Five years later, a teacher wants to perform a hypothesis test to determine whether the average math SAT score of students at the school has changed from the 1990 mean of 510. Formulate the null and alternative hypotheses for the study described.

A skeptical paranormal researcher claims that the proportion of Americans that have seen a UFO, p, is less than 1 in every ten thousand. Assume that a hypothesis test of the claim has been conducted and that the conclusion of the test was to reject the null hypothesis. Identify the population to which the Results of the test apply.

A consumer advocacy group claims that the mean amount of juice in a 16 ounce bottled drink is not 16 ounces, as stated by the bottler. Determine the conclusion of the hypothesis test assuming that the results of the sampling lead to rejection of the null hypothesis.

A two-tailed test is conducted at the 5% significance level. What is the smallest z-score listed below that results in rejection of the null hypothesis?

In 1990, the average duration of long-distance telephone calls originating in one town was $9.4$ minutes. A long-distance telephone company wants to perform a hypothesis test to determine whether the average duration of long-distance phone calls has changed from the 1990 mean of $9.4$ minutes. The mean duration for a random sample of 50 calls originating in the town was $8.6$ minutes. Does the data provide sufficient evidence to conclude that the mean call duration, $\mu$ , is different from the 1990 mean of $9.4$ minutes? Perform the appropriate hypothesis test using a significance level of $0.01$ . Assume that $\sigma=4.8$ minutes.

In the past, the mean running time for a certain type of flashlight battery has been 8.0 hours. The manufacturer has introduced a change in the production method and wants to perform a hypothesis Test to determine whether the mean running time has increased as a result. The hypotheses are: :\mu=8.0 hours :\mu>8.0 hours Explain the meaning of a Type II error.

$\mathrm { H } _ { \mathrm { a } } : \mu > 19.9 , \bar { x } = 23.1 , \sigma = 8 , \mathrm { n } = 100$ . Without computing a $\mathrm { P }$ -value, determine whether the alternate hypothesis is supported and give a reason for your conclusion.

In 1990 , the average duration of long-distance telephone calls originating in one town was $9.4$ minutes. A long-distance telephone company wants to perform a hypothesis test to determine whether the average duration of long-distance phone calls has changed from the 1990 mean of $9.4$ minutes. The mean duration for a random sample of 50 calls originating in the town was $8.6$ minutes. Does the data provide sufficient evidence to conclude that the mean call duration, $\mu$ , has changed from the 1990 mean of $9.4$ minutes? Perform the appropriate hypothesis test using a significance level of $0.01$ . Assume that $\sigma=4.2$ minutes.

A manufacturer claims that the mean amount of juice in its 16 ounce bottles is $16.1$ ounces. A consumer advocacy group wants to perform a hypothesis test to determine whether the mean amount is actually less than this. The mean volume of juice for a random sample of 70 bottles was $15.94$ ounces. Do the data provide sufficient evidence to conclude that the mean amount of juice for all 16ounce bottles, $\mu$ , is less than $16.1$ ounces? Perform the appropriate hypothesis test using a significance level of $0.10$ . Assume that $\sigma=0.9$ ounces.

At one school, the mean amount of time that tenth-graders spend watching television each week is 18.4 hours. The principal introduces a campaign to encourage the students to watch less television. One year later, the principal wants to perform a hypothesis test to determine whether the average amount of time spent watching television per week has decreased. Formulate the null and alternative hypotheses for the study described.

The standard score for a two-tailed test is 2.0. What is the P-value?

A two-tailed test is conducted at the 5% significance level. What is the left tail percentile required to reject the null hypothesis?

A skeptical paranormal researcher claims that the proportion of Americans that have seen a UFO is less than 1 in every one thousand. State the null hypothesis and the alternative hypothesis for a test of Significance.