Exam 10: Hypothesis Tests Regarding a Parameter

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 rejects the null hypothesis?

Test Hypotheses about a Population Mean with Unknown -A shipping firm suspects that the mean life of a certain brand of tire used by its trucks is less than 36,000 miles. To check the claim, the firm randomly selects and tests 18 of these tires and gets a mean lifetime of 35,350 miles with a standard deviation of 1200 miles. At $\alpha = 0.05$ , test the shipping firm's claim.

Test Hypotheses about a Population Mean with Known Using the Classical Approach - $\text { Test the claim that } \mu > 29 \text {, given that } \alpha = 0.05 \text { and the sample statistics are } n = 50 , \bar { x } = 29.3 \text {, and } \sigma = 1.2 \text {. }$

Test Hypotheses about a Population Proportion -In one area, monthly incomes of technology related workers have a standard deviation of $\$ 650$ . It is believed that the standard deviation of monthly incomes of non-technology workers is higher. A sample of 71 non-technology workers are randomly selected and found to have a standard deviation of $\$ 950$ . Test the claim that non-technology workers have a higher standard deviation. Use $\alpha = 0.05$ .

Explain Type I and Type II Errors -The mean age of judges in Los Angeles is $52.7$ years. Identify the type I and type II errors for the hypothesis test of this claim.

State Conclusions to Hypothesis Tests -The mean age of principals in a local school district is $56.7$ years. If a hypothesis test is performed, how should you interpret a decision that rejects the null hypothesis?

Test Hypotheses about a Population Mean with Unknown - $\text { Use a t-test to test the claim } \mu > 39 \text { at } \alpha = 0.005 \text {, given the sample statistics } \mathrm { n } = 25 , \bar { x } = 40 \text {, and } s = 3$

Test Hypotheses about a Population Mean with Known Using the Classical Approach - $\text { Test the claim that } \mu \neq 920 \text {, given that } \alpha = 0.01 \text { and the sample statistics are } n = 35 , \bar { x } = 890 \text {, and } \sigma = 82 \text {. }$

Test Hypotheses about a Population Proportion -A nationwide survey claimed that at least $50 \%$ of parents with young children condone spanking their child as a regular form of punishment. In a random sample of 100 parents with young children, how many would need to say that they condone spanking as a form of punishment in order to refute the claim at $\alpha = 0.5$ ?

Provide an appropriate response. -A _____is a statement or claim regarding a characteristic of one or more populations.

Test Hypotheses about a Population Proportion -A brokerage firm needs information concerning the standard deviation of the account balances of its customers. From previous information it was assumed to be $\$ 250$ . A random sample of 61 accounts was checked. The standard deviation was $\$ 286.20$ . At $\alpha = 0.01$ , test the firm's assumption. Assume that the account balances are normally distributed.

Test Hypotheses about a Population Proportion -Test the claim that $\sigma ^ { 2 } = 34.4$ if $\mathrm { n } = 12 , \mathrm {~s} ^ { 2 } = 28.8$ and $\alpha = 0.05$ . Assume that the population is normally distributed.

State Conclusions to Hypothesis Tests -The mean age of judges in Dallas is greater than $53.6$ years. 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 Known Using the Classical Approach -In a one-tailed test of the hypothesis using the classical method, the critical region is the area under the graph located

Explain Type I and Type II Errors -We never conclude "Accept $\mathrm { H } _ { 0 }$ " in a test of hypothesis. This is because:

Test Hypotheses about a Population Mean with Known Using P-values -Suppose you are using $\alpha = 0.01$ to test the claim that $\mu = 1110$ using a P-value. You are given the sample statistics $\mathrm { n } = 35 , \overline { \mathrm { x } } = 1080$ , and $\sigma = 82$ . Find the $\mathrm { P }$ -value.

State Conclusions to Hypothesis Tests -The mean age of professors at a university is $55.3$ years. 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 Known Using P-values -Given $\mathrm { H } _ { 0 } : \mu \leq 85 , \mathrm { H } _ { 1 } : \mu > 85$ , and $\mathrm { P } = 0.006$ . Do you reject or fail to reject $\mathrm { H } _ { 0 }$ at the $0.01$ level of significance?

Test Hypotheses about a Population Proportion -In 1990, the mean for the number of pets owned per household was 1.9. A poll of 1023 households conducted this year reported the mean for the number of pets owned per household to be 1.8. Assuming $\sigma = 1.1$ , is there sufficient evidence to support the claim that the mean number of pets owned has changed since 1990 at the $\alpha =$ $0.1$ level of significance?

Test Hypotheses about a Population Mean with Unknown - $\text { Use a t-test to test the claim } \mu \leq 2.8 \text { at } \alpha = 0.05 \text {, given the sample statistics } \mathrm { n } = 15 , \overline { \mathrm { x } } = 3.1 \text {, and } \mathrm { s } = 0.8 \text {. }$