Exam 8: Hypothesis Testing

Assume that a simple random sample has been selected from a normally distributed population and test the given claim. Use either the traditional method or P-value method as indicated. Identify the null and alternative hypotheses, test statistic, critical value(s)or P-value (or range of P-values)as appropriate, and state the final conclusion that addresses the original claim. A cereal company claims that the mean weight of the cereal in its packets is 14 oz. The weights (in ounces)of the cereal in a random sample of 8 of its cereal packets are listed below. 14.6 13.8 14.1 13.7 14.0 14.4 13.6 14.2 Test the claim at the 0.01 significance level.

Find the P-value in a test of the claim that the mean IQ score of acupuncturists is equal to 100, given that the test statistic is z =−2.00.

Assume that a hypothesis test of the given claim will be conducted. Identify the type I or type II error for the test. A consumer advocacy group claims that the mean mileage for the Carter Motor Company's new sedan is less than 32 miles per gallon. Identify the type I error for the Test.

Use the given information to find the $P$ -value. Also, use a $0.05$ significance level and state the conclusion about the null hypothesis (reject the null hypothesis or fail to reject the null hypothesis). With $H _ { 1 } : p > 0.554$ , the test statistic is $z = 1.34$ .

Find the P-value for the indicated hypothesis test. 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. Find the P -value for a test of the researcher's Claim.

Solve the problem. For large numbers of degrees of freedom, the critical $\chi ^ { 2 }$ values can be approximated as follows: $\chi ^ { 2 } = \frac { 1 } { 2 } ( z + \sqrt { 2 k - 1 } ) ^ { 2 }$ , where $\mathrm { k }$ is the number of degrees of freedom and $z$ is the critical value. To find the lower critical value, the negative $z$ -value is used, to find the upper critical value, the positive $z$ -value is used. Use this approximation to estimate the critical value of $\chi ^ { 2 }$ in a right-tailed hypothesis test with $n = 143$ and $\alpha = 0.01$ .

A formal hypothesis test is to be conducted using the claim that the mean body temperature is equal to $98.6 ^ { \circ } \mathrm { F }$ . What is the null hypothesis and how is it denoted?

Find the P-value in a test of the claim that the mean College Algebra final exam score of engineering majors equal to 88, given that the test statistic is z = 1.50.

What do you conclude about the claim below? Do not use formal procedures or exact calculations. Use only the rare event rule and make a subjective estimate to determine whether the event is likely. Claim: A die is fair and in 100 rolls there are 63 sixes.

Which of the following is not a requirement for testing a claim about a population proportion?

A formal hypothesis test is to be conducted using the claim that the mean AC thermostat setting in restaurants is equal to $74 ^ { \circ } \mathrm { F }$ . What is the null hypothesis and how is it denoted?

Use the traditional method to test the given hypothesis. Assume that the population is normally distributed and that the sample has been randomly selected. Heights of men aged 25 to 34 have a standard deviation of 2.9. Use a 0.05 significance level to test the claim that the heights of women aged 25 to 34 have a different standard deviation. The heights (in inches)of 16 randomly selected women aged 25 to 34 are listed below. Round the sample standard deviation to five decimal places. 62.13 65.09 64.18 66.72 63.09 61.15 67.50 64.65 63.80 64.21 60.17 68.28 66.49 62.10 65.73 64.72

Formulate the indicated conclusion in nontechnical terms. Be sure to address the original claim. The principal of a middle school claims that test scores of the seventh-graders at his school Vary less than the test scores of the seventh-graders at a neighboring school, which have Variation described by $\sigma = 14.7$ . 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.

Identify the null hypothesis, alternative hypothesis, test statistic, P -value, conclusion about the null hypothesis, and final conclusion that addresses the original claim. 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 234 fathers from Littleton yielded 96 who did not help with child care. Test the researcher's claim at the 0.05 significance level.

Assume that a simple random sample has been selected from a normally distributed population and test the given claim. Use either the traditional method or P-value method as indicated. Identify the null and alternative hypotheses, test statistic, critical value(s)or P-value (or range of P-values)as appropriate, and state the final conclusion that addresses the original claim. A public bus company official claims that the mean waiting time for bus number 14 during peak hours is less than 10 minutes. Karen took bus number 14 during peak hours on 18 different occasions. Her mean waiting time was 7.6 minutes with a standard deviation of 2.3 minutes. At the 0.01 significance level, test the claim that the mean waiting time is less than 10 minutes. Use the P-value method of testing hypotheses.

Express the null hypothesis and the alternative hypothesis in symbolic form. Use the correct symbol $( \mu , p , \sigma )$ for the indicated parameter. An entomologist writes an article in a scientific journal which claims that fewer than 16 in ten thousand male fireflies are unable to produce light due to a genetic mutation. Use the parameter $p$ , the true proportion of fireflies unable to produce light.

Use the given information to find the $P$ -value. Also, use a $0.05$ significance level and state the conclusion about the null hypothesis (reject the null hypothesis or fail to reject the null hypothesis). With $H _ { 1 } : p \neq 3 / 5$ , the test statistic is $z = 0.78$ .

Use the given information to find the P-value. Also, use a 0.05 significance level and state the conclusion about the null hypothesis (reject the null hypothesis or fail to reject the null Hypothesis). The test statistic in a right-tailed test is z = 0.52.

A watch manufacturer believes that $60 \%$ of men over age 50 wear watches. So, the manufacturer took a simple random sample of 275 men over age 50 and 170 of those men wore watches. Test the watch manufacturer's claim at $\alpha = .05$ .

Assume that a simple random sample has been selected from a normally distributed population and test the given claim. Use either the traditional method or P-value method as indicated. Identify the null and alternative hypotheses, test statistic, critical value(s)or P-value (or range of P-values)as appropriate, and state the final conclusion that addresses the original claim. A light-bulb manufacturer advertises that the average life for its light bulbs is 900 hours. A random sample of 15 of its light bulbs resulted in the following lives in hours. 995 590 510 539 739 917 571 555 916 728 664 693 708 887 849 At the 10% significance level, test the claim that the sample is from a population with a mean life of 900 hours. Use the P-value method of testing hypotheses.