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A random sample of 25 values is drawn from a mound-shaped and symmetric distribution. The sample mean is 10 and the sample standard deviation is 2. Use a level of significance of 0.05 to conduct a two-tailed test of the claim that the population mean is 9.5. (a) Is it appropriate to use a Student's t distribution? Explain. Yes, because the distribution is mound-shaped and symmetric, and σ is unknown. How many degrees of freedom do we use? (b) What are the hypotheses? H0: μ = 9.5; H1: μ ≠ 9.5 (c) Compute the t value of the sample test statistic. (Round your answer to three decimal places.) t = (d) Estimate the P-value for the test. P-value > 0.250 0.100 < P-value < 0.250 0.050 < P-value < 0.100 0.010 < P-value < 0.050 P-value < 0.010 (e) Do we reject or fail to reject H0? At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. (f) Interpret the results. There is insufficient evidence at the 0.05 level to reject the null hypothesis. A random sample of 25 values is drawn from a mound-shaped and symmetric distribution. The sample mean is 10 and the sample standard deviation is 2. Use a level of significance of 0.05 to conduct a two-tailed test of the claim that the population mean is 9.5. (a) Is it appropriate to use a Student's t distribution? Explain. Yes, because the distribution is mound-shaped and symmetric, and σ is unknown. How many degrees of freedom do we use? (b) What are the hypotheses? H0: μ = 9.5; H1: μ ≠ 9.5 (c) Compute the t value of the sample test statistic. (Round your answer to three decimal places.) t = (d) Estimate the P-value for the test. P-value > 0.250 0.100 < P-value < 0.250 0.050 < P-value < 0.100 0.010 < P-value < 0.050 P-value < 0.010 (e) Do we reject or fail to reject H0? At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. (f) Interpret the results. There is insufficient evidence at the 0.05 level to reject the null hypothesis. Show more…

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Elementary Statistics a Step by Step Approach Allan G. Bluman 9th Edition

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Yes, it is appropriate to use a Student's t distribution because the sample size is less than 30, and the population standard deviation is unknown. How many degrees of freedom do we use? The degrees of freedom are n-1, where n is the sample size. Show more…

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Submit Thanks for your feedback! A random sample of 25 values is drawn from a mound-shaped and symmetric distribution. The sample mean is 10 and the sample standard deviation is 2. Use a level of significance of 0.05 to conduct a two-tailed test of the claim that the population mean is 9.5. (a) Is it appropriate to use a Student's t distribution? Explain. Yes, because the distribution is mound-shaped and symmetric, and σ is unknown. How many degrees of freedom do we use? (b) What are the hypotheses? H0: μ = 9.5; H1: μ ≠ 9.5 (c) Compute the t value of the sample test statistic. (Round your answer to three decimal places.) t = (d) Estimate the P-value for the test. P-value > 0.250 0.100 < P-value < 0.250 0.050 < P-value < 0.100 0.010 < P-value < 0.050 P-value < 0.010 (e) Do we reject or fail to reject H0? At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. (f) Interpret the results. There is insufficient evidence at the 0.05 level to reject the null hypothesis. Play audio Feedback Powered by NumerAI

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A random sample of 25 values is drawn from a mound-shaped and symmetric distribution. The sample mean is 9 and the sample standard deviation is 2. Use a level of significance of 0.05 to conduct a two-tailed test of the claim that the population mean is 8.5. (a) Is it appropriate to use a Student's t distribution? Explain. Yes, because the x distribution is mound-shaped and symmetric and σ is unknown. No, the x distribution is skewed left. No, the x distribution is skewed right. No, the x distribution is not symmetric. No, σ is known. How many degrees of freedom do we use? (b) What are the hypotheses? H0: μ = 8.5; H1: μ ≠ 8.5 H0: μ = 8.5; H1: μ > 8.5 H0: μ > 8.5; H1: μ = 8.5 H0: μ < 8.5; H1: μ = 8.5 H0: μ = 8.5; H1: μ < 8.5 (c) Compute the t value of the sample test statistic. (Round your answer to three decimal places.) t = (d) Estimate the P-value for the test. P-value > 0.250 0.100 < P-value < 0.250 0.050 < P-value < 0.100 0.010 < P-value < 0.050 P-value < 0.010 (e) Do we reject or fail to reject H0? At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant. At the α = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant. At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant. At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. (f) Interpret the results. There is sufficient evidence at the 0.05 level to reject the null hypothesis. There is insufficient evidence at the 0.05 level to reject the null hypothesis.

Adi S.

A random sample of 25 values is drawn from a mound-shaped and symmetric distribution. The sample mean is 11 and the sample standard deviation is 2. Use a level of significance of 0.05 to conduct a two-tailed test of the claim that the population mean is 10.5. (a) Is it appropriate to use a Student's t distribution? Explain. Yes, because the distribution is mound-shaped and symmetric, and 𝜎 is unknown. How many degrees of freedom do we use? (b) What are the hypotheses? H0: 𝜇 = 10.5; H1: 𝜇 ≠ 10.5 (c) Compute the t value of the sample test statistic. (Round your answer to three decimal places.) t = (d) Estimate the P-value for the test. P-value > 0.250 0.100 < P-value < 0.250 0.050 < P-value < 0.100 0.010 < P-value < 0.050 P-value < 0.010 (e) Do we reject or fail to reject H0? At the 𝛼 = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. (f) Interpret the results. There is insufficient evidence at the 0.05 level to reject the null hypothesis.

Adi S.

A random sample of 25 values is drawn from a mound-shaped and symmetric distribution. The sample mean is 10 and the sample standard deviation is $2 .$ Use a level of significance of 0.05 to conduct a two-tailed test of the claim that the population mean is $9.5 .$ (a) Is it appropriate to use a Student's $t$ distribution? Explain. How many degrees of freedom do we use? (b) What are the hypotheses? (c) Compute the $t$ value of the sample test statistic. (d) Estimate the $P$ -value for the test. (e) Do we reject or fail to reject $H_{0} ?$ (f) Interpret the results.

Hypothesis Testing

Testing the Mean $\mu$

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