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(a) Determine the critical value for a right-tailed test of a population standard deviation with 18 degrees of freedom at the \(\alpha=0.05\) level of significance. (b) Determine the critical value for a left-tailed test of a population standard deviation for a sample of size \(n=23\) at the \(\alpha=0.1\) level of significance. (c) Determine the critical values for a two-tailed test of a population standard deviation for a sample of size \(n=30\) at the \(\alpha=0.05\) level of significance.

(a) Determine the critical value for a right-tailed test of a population standard deviation with 16 degrees of freedom at the \(\alpha=0.01\) level of significance. (b) Determine the critical value for a left-tailed test of a population standard deviation for a sample of size \(n=14\) at the \(\alpha=0.01\) level of significance. (c) Determine the critical values for a two-tailed test of a population standard deviation for a sample of size \(n=61\) at the \(\alpha=0.05\) level of significance.

To test \(H_{0}: p=0.30\) versus \(H_{1}: p<0.30,\) a simple random sample of \(n=300\) individuals is obtained and \(x=86\) successes are observed. (a) What does it mean to make a Type II error for this test? (b) If the researcher decides to test this hypothesis at the \(\alpha=0.05\) level of significance, compute the probability of making a Type II error if the true population proportion is \(0.28 .\) What is the power of the test? (c) Redo part (b) if the true population proportion is 0.25 .

To test \(H_{0}: \sigma=35\) versus \(H_{1}: \sigma>35,\) a random sample of size \(n=15\) is obtained from a population that is known to be normally distributed. (a) If the sample standard deviation is determined to be \(s=37.4,\) compute the test statistic. (b) If the researcher decides to test this hypothesis at the \(\alpha=0.01\) level of significance, determine the critical value. (c) Draw a chi-square distribution and depict the critical region. (d) Will the researcher reject the null hypothesis? Why?

To test \(H_{0}: p=0.40\) versus \(H_{1}: p>0.40,\) a simple random sample of \(n=200\) individuals is obtained and \(x=84\) successes are observed. (a) What does it mean to make a Type II error for this test? (b) If the researcher decides to test this hypothesis at the \(\alpha=0.05\) level of significance, compute the probability of making a Type II error if the true population proportion is 0.44. What is the power of the test? (c) Redo part (b) if the true population proportion is 0.47

To test \(H_{0}: \mu=100\) versus \(H_{1}: \mu \neq 100,\) a simple random sample of size \(n=23\) is obtained from a population that is known to be normally distributed. (a) If \(\bar{x}=104.8\) and \(s=9.2,\) compute the test statistic. (b) If the researcher decides to test this hypothesis at the \(\alpha=0.01\) level of significance, determine the critical values. (c) Draw a \(t\) -distribution that depicts the critical region. (d) Will the researcher reject the null hypothesis? Why? (e) Construct a \(99 \%\) confidence interval to test the hypothesis.

If we do not reject the null hypothesis when the statement in the alternative hypothesis is true, we have made a Type ____ error.

To test \(H_{0}: \mu=20\) versus \(H_{1}: \mu<20,\) a simple random sample of size \(n=18\) is obtained from a population that is known to be normally distributed. (a) If \(\bar{x}=18.3\) and \(s=4.3,\) compute the test statistic. (b) Draw a \(t\) -distribution with the area that represents the \(P\) -value shaded. (c) Approximate and interpret the \(P\) -value. (d) If the researcher decides to test this hypothesis at the \(\alpha=0.05\) level of significance, will the researcher reject the null hypothesis? Why?

To test \(H_{0}: \sigma=4.3\) versus \(H_{1}: \sigma \neq 4.3,\) a random sample of size \(n=12\) is obtained from a population that is known to be normally distributed. (a) If the sample standard deviation is determined to be \(s=4.8\), compute the test statistic. (b) If the researcher decides to test this hypothesis at the \(\alpha=0.05\) level of significance, determine the critical values. (c) Draw a chi-square distribution and depict the critical regions. (d) Will the researcher reject the null hypothesis? Why?

To test \(H_{0}: \sigma=1.2\) versus \(H_{1}: \sigma \neq 1.2,\) a random sample of size \(n=22\) is obtained from a population that is known to be normally distributed. (a) If the sample standard deviation is determined to be \(s=0.8\), compute the test statistic. (b) If the researcher decides to test this hypothesis at the \(\alpha=0.10\) level of significance, determine the critical values. (c) Draw a chi-square distribution and depict the critical regions. (d) Will the researcher reject the null hypothesis? Why?