Exam 7: Hypothesis Testing With One Sample

Test the claim about the population mean μ at the level of significance α. Assume the population is normally distributed. Claim: $\mu \leq 47 ; \alpha = 0.01 ; \sigma = 4.3$ Sample statistics: $\bar { x } = 48.8 , n = 40$

Given $\mathrm { H } _ { 0 } : \mu \leq 12$ for which confidence interval should you reject $\mathrm { H } _ { 0 } ?$

A local group claims that the police issue more than 60 speeding 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 α $\alpha$ = 0.01, test the groupʹs claim using P-values. 70 48 41 68 69 55 70 57 60 83 32 60 72 58

Test the claim that $\mu = 740 \text {, }$ given that $\sigma = 82 , \alpha = 0.01$ and the sample statistics are n = $35 \text { and } \bar { x } = 710$

Test the claim about the population mean μ at the level of significance α $\alpha$ Assume the population is normally distributed. Claim: $\mu = 1400 ; \alpha = 0.01 ; \sigma = 82$ Sample statistics: $\bar { x } = 1370 , n = 35$

Find the critical value and rejection region for the type of chi-square test with sample size n and level of significance α $\alpha$ Two-tailed test, $\mathrm { n } = 10 , \alpha = 0.01$ Find the critical $x ^ { 2 }$ - valuevalues to test the claim $\sigma ^ { 2 } \neq 6.8$ if n = 10 and α $\alpha$ = 0.01.

The buyer of a local hiking club store recommends against buying the new digital altimeters because they vary more than the old altimeters, which had a standard deviation of one yard. State this claim mathematically. Write the null and alternative hypotheses. Identify which hypothesis is the claim.

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

The statement represents a claim. Write its complement and state which is $\mathrm { H } _ { 0 }$ and which is $\mathrm { H } _ { \mathrm { A } }$ $p \leq$ .93

A trucking firm suspects that the variance for a certain tire is greater than 1,000,000. To check the claim, the firm puts 101 of these tires on its trucks and gets a standard deviation of 1200 miles. At α $\alpha$ = 0.05, test the trucking firmʹs claim.

A car maker claims that its new sub-compact car gets better than 49 miles per gallon on the highway. Determine whether the hypothesis test for this is left-tailed, right-tailed, or two-tailed.

Find the P-value for the hypothesis test with the standardized test statistic z. Decide whether to reject $\mathrm { H } _ { 0 }$ for the level of significance α $\alpha .$ Left-tailed test Z = -2.05 $\alpha$ = 0.05 The test statistic in a left-tailed test is z = -2.05.

The mean IQ of statistics teachers is greater than 130. If a hypothesis test is performed, how should you interpret a decision that rejects the null hypothesis?

Find the standardized test statistic t for a sample with $\mathrm { n } = 20 , \overline { \mathrm { x } } = 6.9 , \mathrm {~s} = 2.0 \text {, and } \alpha = 0.05 \text { if } \mathrm { H } _ { \mathrm { a } } : \mu < 7.3 \text {. Round }$ your answer to three decimal places.

A manufacturer claims that the mean lifetime of its fluorescent bulbs is 1500 hours. A homeowner selects 40 bulbs and finds the mean lifetime to be 1480 hours with a population standard deviation of 80 hours. Test the manufacturerʹs claim. Use $\alpha$ = 0.05.

A manufacturer claims that the mean lifetime of its fluorescent bulbs is 1000 hours. A homeowner selects 25 bulbs and finds the mean lifetime to be 980 hours with a standard deviation of 80 hours. If α $\alpha$ = 0.05, test the manufacturerʹs claim using P-values.

Find the critical value and rejection region for the type of chi-square test with sample size n and level of significance α $\alpha$ Left-tailed test, $\mathrm { n } = 15 , \alpha = 0.05$

The mean age of bus drivers in Chicago is 50.3 years. If a hypothesis test is performed, how should you interpret a decision that fails to reject the null hypothesis?

A local bank needs information concerning the standard deviation of the checking 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 α $\alpha$ = 0.01, test the bankʹs assumption. Assume that the account balances are normally distributed.

The heights (in inches)of 20 randomly selected adult males are listed below. Test the claim that the variance is less than 6.25. Use $\alpha$ = 0.05. Assume the population is normally distributed. 70 72 71 70 69 73 69 68 70 71 67 71 70 74 69 68 71 71 71 72