Exam 10: Hypothesis Tests Regarding a Parameter

Test Hypotheses about a Population Proportion -If $\beta$ is computed to be $0.763$ , then the power of the test is

Test Hypotheses about a Population Mean with Unknown -A bank claims that the mean waiting time in line is less than $2.2$ minutes. A random sample of 20 customers has a mean of 2 minutes with a standard deviation of $0.8$ minute. If $\alpha = 0.05$ , test the bank's claim using $\mathrm { P }$ -values.

State Conclusions to Hypothesis Tests -A candidate for state representative of a certain state claims to be favored by at least half of the voters. If a hypothesis test is performed, how should you interpret a decision that fails to reject the null hypothesis?

Test Hypotheses about a Population Mean with Unknown -A local juice manufacturer distributes juice in bottles labeled 12 ounces. A government agency thinks that the company is cheating its customers. The agency selects 20 of these bottles, measures their contents, and obtains a sample mean of $11.7$ ounces with a standard deviation of $0.7$ ounce. Use a $0.01$ significance level to test the agency's claim that the company is cheating its customers.

Test Hypotheses about a Population Mean with Unknown -Find the standardized test statistic t for a sample with $\mathrm { n } = 20 , \bar { x } = 11.2 , \mathrm {~s} = 2.0$ , and $\alpha = 0.05$ if $\mathrm { H } _ { 1 } : \mu < 11.6$ . Round your answer to three decimal places.

Explain the Logic of Hypothesis Testing -When the results of a hypothesis test are determined to be statistically significant, then we_____ the null hypothesis.

Test Hypotheses about a Population Mean with Known Using the Classical Approach -You wish to test the claim that $\mu > 21$ at a level of significance of $\alpha = 0.05$ and are given sample statistics $n = 50$ , $\bar { x } = 21.3$ , and $\sigma = 1.2$ . Compute the value of the test statistic. Round your answer to two decimal places.

Explain the Logic of Hypothesis Testing -Suppose you want to test the claim that $\mu = 3.5$ . Given a sample size of $\mathrm { n } = 32$ and a level of significance of $\alpha = 0.01$ , when should you reject $\mathrm { H } _ { 0 }$ ?

Test Hypotheses about a Population Proportion - $\text { A coin is tossed } 1000 \text { times and } 570 \text { heads appear. At } \alpha = 0.05 \text {, test the claim that this is not a biased coin. }$

Test Hypotheses about a Population Mean with Known Using the Classical Approach -A local group claims that the police issue at least 60 parking tickets a day in their area. To prove their point, they randomly select one month. Their research yields the number of tickets issued for each day. The data are listed below. At $\alpha = 0.01$ , test the group's claim. 70 48 41 68 69 55 70 57 60 83 32 60 72 58 88 48 59 60 56 65 66 60 68 42 57 59 49 70 75 63 44

Test Hypotheses about a Population Mean with Unknown -A local group claims that the police issue at least 60 parking tickets a day in their area. To prove their point, they randomly select two weeks. Their research yields the number of tickets issued for each day. The data are listed below. At $\alpha = 0.01$ , test the group's claim. 70 48 41 68 69 55 70 57 60 83 32 60 72 58

Test Hypotheses about a Population Mean with Known Using the Classical Approach -A local juice manufacturer distributes juice in bottles labeled 32 ounces. A government agency thinks that the company is cheating its customers. The agency selects 50 of these bottles, measures their contents, and obtains a sample mean of $31.6$ ounces with a standard deviation of $0.70$ ounce. Use a $0.01$ significance level to test the agency's claim that the company is cheating its customers.

Test Hypotheses about a Population Mean with Unknown -Find the standardized test statistic t for a sample with $\mathrm { n } = 12 , \overline { \mathrm { x } } = 15.2 , \mathrm {~s} = 2.2$ , and $\alpha = 0.01$ if $\mathrm { H } _ { 0 } : \mu = 14$ . Round your answer to three decimal places.

Test Hypotheses about a Population Proportion -It is desired to test $\mathrm { H } _ { 0 } : \mu = 45$ against $\mathrm { H } _ { 1 } : \mu < 45$ using $\alpha = 0.10$ . The population in question is uniformly distributed with a standard deviation of 15. A random sample of 49 will be drawn from this population. If $\mu$ is really equal to 40 , what is the probability that the hypothesis test would lead the investigator to commit a Type II error?

Explain Type I and Type II Errors -True or False: Type I and Type II errors are independent events.

Test Hypotheses about a Population Proportion - $\text { Test the claim that } \sigma \geq 6.7 \text { if } \mathrm { n } = 15 , \mathrm {~s} = 6.1 \text {, and } \alpha = 0.05 \text {. Assume that the population is normally distributed. }$

Test Hypotheses about a Population Mean with Unknown - $\text { Use a t-test to test the claim } \mu = 15.3 \text { at } \alpha = 0.01 \text {, given the sample statistics } \mathrm { n } = 12 , \overline { \mathrm { x } } = 14.8 \text {, and } \mathrm { s } = 2.1 \text {. }$

Test Hypotheses about a Population Mean with Known Using the Classical Approach -A manufacturer claims that the mean lifetime of its lithium battery is 1500 hours. A homeowner selects 40 batteries and finds the mean lifetime to be 1490 hours with a standard deviation of 80 hours. Test the manufacturer's claim. Use $\alpha = 0.05$ .

Test Hypotheses about a Population Mean with Known Using P-values -Suppose you are using $\alpha = 0.01$ to test the claim that $\mu \leq 47$ using a P-value. You are given the sample statistics $\mathrm { n } = 40 , \overline { \mathrm { x } } = 48.8$ , and $\sigma = 4.3$ . Find the $\mathrm { P }$ -value.

Test Hypotheses about a Population Mean with Unknown -A local retailer claims that the mean waiting time is less than 8 minutes. A random sample of 20 waiting times has a mean of $6.5$ minutes with a standard deviation of $2.1$ minutes. At $\alpha = 0.01$ , test the retailer's claim. Assume the distribution is normally distributed.