Exam 8: Hypothesis Testing

Find the critical value or values of $\chi ^ { 2 }$ based on the given information. $H _ { 1 } : \sigma < 0.14$ n=23 $\alpha = 0.10$

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.

Find the value of the test statistic z using $z = \frac { \hat { p } - p } { \sqrt { \frac { p q } { n } } }$ A claim is made that the proportion of children who play sports is less than 0.5 , and the sample statistics include n=1320 subjects with 30 % saying that they play a sport.

Express the original claim in symbolic form. Claim: 60% of homes have smoke detectors.

A _____________ error is the mistake of rejecting the null hypothesis when it is actually true

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.

Solve the problem. Use the P-value method to test the claim that the population standard deviation of the systolic blood pressures of adults aged 40-50 is equal to 22 mm Hg. The sample statistics are as follows: n=23, x=132.2 mm Hg, s=26.6 mm Hg. Be sure to state the hypotheses, the value of this test statistic, the P -value, and your conclusion. Use a significance level of 0.05 .

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 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 $x ^ { 2 }$ in a two-tailed hypothesis test with n=104 and $\alpha = 0.10$

A Type I error is the mistake of ________________ when it is actually true

An oil change shop claims that they will change your oil in under 15 minutes. To test this claim, a consumer advocacy group takes a simple random sample of 10 customers and records the number of minutes it took to complete oil changes for these customers. Assume that oil change times are normally distributed. Minutes for Oil Change 8 2 7 12 14 11 25 8 43 15 Conduct a hypothesis test for the oil shop's claim about oil change times at the 5% level of significance.

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

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 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 $x ^ { 2 }$ in a right-tailed hypothesis test with n=143 and $\alpha = 0.01$

Sam wanted to test a claim about the mean of a population whose standard deviation was unknown. He picked a simple random sample of size 20 from the population. Lou wanted to test a claim about a mean of a different population whose standard deviation was known. He picked a simple random sample of size 22 from that population. George said that Sam would need to determine whether his sample was from a normally distributed population because the population standard deviation was unknown. He said that Lou would not need to do this since for his test the population standard deviation was known. Is George right? 116

The p-value is the probability of getting a test statistic at least as extreme as the one representing the sample data, assuming that ______________________________.

Solve the problem. 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 roulette wheel is fair and in 40 consecutive spins of the wheel, black shows up 23 times. (A roulette wheel has 38 equally likely slots of which 18 are black).

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.

Suppose we want to test the claim that the majority of adults are in favor of raising the voting age to 21. Is the hypothesis test left-tailed, right-tailed, or two-tailed?

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 $H _ { 1 } : p \neq 0.377$ the test statistic is z=3.06 .

A hypothesis test is performed to test the claim that a population proportion is greater than 0.7 . Find the probability of a type II error $\beta$ given that the true value of the population proportion is 0.72 . The sample size is 50 and the significance level is 0.05 .

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 .