Exam 9: Hypothesis Testing

Conduct a full hypothesis test and determine if the given claim is supported or not supported at the 0.05 significance level. Round all amounts and standard scores to two decimal places. -According to a recent poll 53% of Americans would vote for the incumbent president. If a random sample of 100 people results in 25% who would vote for the incumbent, test whether the claim that the actual percentage is different from 53% is supported or not supported.

Use the partial table below to find the P-value that corresponds to the standard z-score, and determine whether the alternative hypothesis is supported or not supported at the 0.05 significance level. $\underline{\text { Standard Score and Percentiles for a Normal Distribution }}$ \ -3.5 0.02 -1.0 15.87 1.5 93.32 -3.0 0.13 -0.5 30.85 2.0 97.72 -2.5 0.62 0.0 50.00 2.5 99.38 -2.0 2.28 0.5 69.15 3.0 99.87 -1.5 6.68 1.0 84.13 3.5 99.98 - $\mathrm { z } = - 0.5 \text { for } \mathrm { H } _ { \mathrm { a } } : \mu < 60$

Conduct a full hypothesis test and determine if the given claim is supported or not supported at the 0.05 significance level. Round all amounts and standard scores to two decimal places. -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. Test whether the claim that the mean call duration has changed from the 1990 mean of 9.4 minutes is supported or not supported. Assume that the Population standard deviation is 4.5 minutes.

Find the value of the standard score, z, and determine whether the alternative hypothesis is supported or not supported at a 0.05 significance level. - $\mathrm { H } _ { \mathrm { a } } : \mu > 50 , \mathrm { n } = 55 , \overline { \mathrm { x } } = 51 , \sigma = 3.6$

Conduct a full hypothesis test and determine if the given claim is supported or not supported at the 0.05 significance level. Round all amounts and standard scores to two decimal places. -An article in a journal reports that 34% of American fathers take no responsibility for child care. A researcher Claims that the figure is higher for fathers in the town of Littleton. A random sample of 225 fathers from Littleton yielded 97 who did not help with child care. Test whether the researcher's claim that the percentage is Higher than 34% is supported or not supported.

Conduct a full hypothesis test and determine if the given claim is supported or not supported at the 0.05 significance level. Round all amounts and standard scores to two decimal places. -A manufacturer considers his production process to be out of control when defects exceed 3%. In a random sample of 85 items, the defect rate is 5.8% but the manager claims that this is only a sample fluctuation and production is not really out of control. Test whether the manufacturer's claim that production is out of control is supported or not supported.

Use a 0.05 significance level and conduct a full hypothesis test. List the null and alternative hypotheses, the z-score, the P-value, and whether to reject or not reject the null hypothesis. Round z-scores to the nearest tenth. -A national car insurance company stated that in 1987, the average yearly car insurance cost for a family in the U.S. was $1716. In the same year, a random sample of 32 families in California resulted in a mean cost of $1728 with a standard deviation of $35.50. Test the claim that the average insurance cost for a family in California in 1987 exceeded the national average.

In 1990, the average duration of long-distance telephone calls originating in one town was 8.5 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 8.5 minutes.

Conduct a full hypothesis test and determine if the given claim is supported or not supported at the 0.05 significance level. Round all amounts and standard scores to two decimal places. -A supplier of 3.5" disks claims that no more than 1% of the disks are defective. In a random sample of 700 disks, it is found that 3% are defective, but the supplier claims that this is only a sample fluctuation. Test whether the supplier's claim that no more than 1% are defective is supported or not supported.

A manufacturer wishes to test the claim that one of its pancake mixes has a mean weight that does not equal 16 ounces as advertised.

Find the value of the standard score, z, and determine whether the alternative hypothesis is supported or not supported at a 0.05 significance level. - $\mathrm { H } _ { \mathrm { a } } : \mu \neq 18.7 , \mathrm { n } = 11 , \overline { \mathrm { x } } = 20.5 , \sigma = 7$

Conduct a full hypothesis test and determine if the given claim is supported or not supported at the 0.05 significance level. Round all amounts and standard scores to two decimal places. -In one city, the average amount of time that tenth-graders spend watching television each week is 22.4 hours. the principal of Birchwood High School believes that at his school, tenth-graders watch less television. For a Sample of 32 tenth-graders from Birchwood High School, the mean amount of time spent watching television per week was 20.2 hours. Test whether the claim that for all tenth-graders at Birchwood High School, the mean Amount of time spent watching television per week is less than the city average of 22.4 hours is supported or not supported. Assume that $\sigma = 7.2$ Hours.

Conduct a full hypothesis test and determine if the given claim is supported or not supported at the 0.05 significance level. Round all amounts and standard scores to two decimal places. -In 1990, the average math SAT score for students at one school was 475. 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. He picks a random sample of 60 students and obtains their mean math SAT score, which is 469. Test whether the claim that the average math SAT score at the school has dropped from 475 is supported or not Supported. Assume that $\sigma = 73$

Answer the question. -A study of a brand of "in the shell" peanuts sold at sports events gives the following results: Number of Peanuts per bag balprobability 25 0.003 30 0.02 35 0.09 40 0.15 45 0.35 50 0.217 55 0.07 A fan purchased a bag with 30 peanuts. What is the P-value for this result?

Use the partial table below to find the P-value that corresponds to the standard z-score, and determine whether the alternative hypothesis is supported or not supported at the 0.05 significance level. $\underline{\text { Standard Score and Percentiles for a Normal Distribution }}$ \ -3.5 0.02 -1.0 15.87 1.5 93.32 -3.0 0.13 -0.5 30.85 2.0 97.72 -2.5 0.62 0.0 50.00 2.5 99.38 -2.0 2.28 0.5 69.15 3.0 99.87 -1.5 6.68 1.0 84.13 3.5 99.98 - $\mathrm { z } = - 2.5$ for $\mathrm { H } _ { \mathrm { a } } : \mu < 22$

Solve the problem. -The manufacturer of a refrigerator system for beer kegs produces refrigerators that are supposed to maintain a mean temperature of 48°F, ideal for a certain type of German pilsner. The owner of the brewery does not agree with the refrigerator manufacturer, and claims he can prove that the mean temperature of the refrigerators is different from 48°F. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is to reject the null hypothesis, state the conclusion in nontechnical terms.

Solve the problem. -A researcher claims that the amounts of acetaminophen in a certain brand of cold tablets have a standard deviation different from the 3.1 milligrams claimed by the manufacturer. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is failure to reject the null hypothesis, state the conclusion in nontechnical terms.

Use a 0.05 significance level and conduct a full hypothesis test. List the null and alternative hypotheses, the z-score, the P-value, and whether to reject or not reject the null hypothesis. Round z-scores to the nearest tenth. -A department store accepts only its own credit card. Among 36 randomly selected card holders, it was found that the mean amount owed was $175.37, while the standard deviation was $84.77. Test the claim that the mean amount owed by all customers is greater than $150.00.

Find the P-value for the indicated hypothesis test. Round all proportions and standard scores to two decimal places. -A random sample of 140 forty-year-old men contains 26% who smoke. Find the P-value for a test of the claim that the percentage of forty-year-old men that smoke is 22%.

Use the partial table below to find the P-value that corresponds to the standard z-score, and determine whether the alternative hypothesis is supported or not supported at the 0.05 significance level. $\underline{\text { Standard Score and Percentiles for a Normal Distribution }}$ \ -3.5 0.02 -1.0 15.87 1.5 93.32 -3.0 0.13 -0.5 30.85 2.0 97.72 -2.5 0.62 0.0 50.00 2.5 99.38 -2.0 2.28 0.5 69.15 3.0 99.87 -1.5 6.68 1.0 84.13 3.5 99.98 - $z = 2.0 \text { for } H _ { a } : \mu > 31.28$