Question

In: Statistics and Probability

Consider the following hypotheses: H0: μ ≤ 12.6 HA: μ > 12.6 A sample of 25...

Consider the following hypotheses:

H0: μ ≤ 12.6

HA: μ > 12.6

A sample of 25 observations yields a sample mean of 13.4. Assume that the sample is drawn from a normal population with a population standard deviation of 3.2.

a. Calculate the value of the test statistic.

b. Find the p-value.

c. Calculate the critical value using α = 0.05

d. What is the conclusion if α = 0.05? Interpret the results at α = 0.05.

e. Calculate the p-value if the above sample mean was based on a sample of 100 observations.

f. Based on a sample of 100 observations, what is the conclusion if α = 0.10? Interpret the results at α = 0.10.

Solutions

Expert Solution

Dear students , please like it.

Thanks.


Related Solutions

Consider the following hypotheses: H0: μ ≤ 42.2 HA: μ > 42.2 A sample of 25...
Consider the following hypotheses: H0: μ ≤ 42.2 HA: μ > 42.2 A sample of 25 observations yields a sample mean of 43.2. Assume that the sample is drawn from a normal population with a population standard deviation of 6.0. a-1. Find the p-value. p-value < 0.01 0.01  p-value < 0.025 0.025  p-value < 0.05 0.05  p-value < 0.10 p-value  0.10 a-2. What is the conclusion if α = 0.10?    Reject H0 since the p-value is greater than α. Reject H0 since the...
Consider the following hypotheses: H0: μ ≥ 180 HA: μ < 180 A sample of 83...
Consider the following hypotheses: H0: μ ≥ 180 HA: μ < 180 A sample of 83 observations results in a sample mean of 175. The population standard deviation is known to be 21. (You may find it useful to reference the appropriate table: z table or t table) a-1. Calculate the value of the test statistic. (Negative value should be indicated by a minus sign. Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal...
Consider the following hypotheses: H0: μ ≥ 199 HA: μ < 199 A sample of 98...
Consider the following hypotheses: H0: μ ≥ 199 HA: μ < 199 A sample of 98 observations results in a sample mean of 195. The population standard deviation is known to be 32. Calculate the value of the test statistic. a-2. Find the p-value. 0.025 p-value < 0.05 0.05 p-value < 0.10 p-value greater than or equal to 0.10 p-value < 0.01 p-value < 0.025 b. Does the above sample evidence enable us to reject the null hypothesis at α...
Consider the following hypotheses: H0: μ ≥ 208 HA: μ < 208 A sample of 74...
Consider the following hypotheses: H0: μ ≥ 208 HA: μ < 208 A sample of 74 observations results in a sample mean of 202. The population standard deviation is known to be 26. (You may find it useful to reference the appropriate table: z table or t table) a-1. Calculate the value of the test statistic. (Negative value should be indicated by a minus sign. Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal...
Consider the following hypotheses: H0: μ ≥ 205 HA: μ < 205 A sample of 83...
Consider the following hypotheses: H0: μ ≥ 205 HA: μ < 205 A sample of 83 observations results in a sample mean of 202. The population standard deviation is known to be 33. (You may find it useful to reference the appropriate table: z table or t table) a-1. Calculate the value of the test statistic. (Negative value should be indicated by a minus sign. Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal...
Consider the following hypotheses: H0: μ ≥ 150 HA: μ < 150 A sample of 80...
Consider the following hypotheses: H0: μ ≥ 150 HA: μ < 150 A sample of 80 observations results in a sample mean of 144. The population standard deviation is known to be 28. Use Table 1. a. What is the critical value for the test with α = 0.01 and with α = 0.05? (Negative values should be indicated by a minus sign. Round your answers to 2 decimal places.) Critical Value   α = 0.01   α = 0.05 b-1. Calculate...
Consider the following hypothesis test. H0: μ ≤ 25 Ha: μ > 25 A sample of...
Consider the following hypothesis test. H0: μ ≤ 25 Ha: μ > 25 A sample of 40 provided a sample mean of 26.1. The population standard deviation is 6. (a) Find the value of the test statistic. (Round your answer to two decimal places.) (b) Find the p-value. (Round your answer to four decimal places.) p-value = (c) At α = 0.01,state your conclusion. (d) State the critical values for the rejection rule. (Round your answer to two decimal places....
Consider the following hypothesis test. H0: μ ≤ 25 Ha: μ > 25 A sample of...
Consider the following hypothesis test. H0: μ ≤ 25 Ha: μ > 25 A sample of 40 provided a sample mean of 26.6. The population standard deviation is 6. (a) Find the value of the test statistic. (Round your answer to two decimal places.) (b) Find the p-value. (Round your answer to four decimal places.) 1) p-value = (c) At  α = 0.01, state your conclusion. 1) Reject H0. There is sufficient evidence to conclude that μ > 25. 2) Reject...
Consider the following hypothesis test. H0: μ ≤ 25 Ha: μ > 25 A sample of...
Consider the following hypothesis test. H0: μ ≤ 25 Ha: μ > 25 A sample of 40 provided a sample mean of 26.6. The population standard deviation is 6. (a) Find the value of the test statistic. (Round your answer to two decimal places.) (b) Find the p-value. (Round your answer to four decimal places.) p-value = (c) At α = 0.01,state your conclusion. Chose one of the following. Reject H0. There is sufficient evidence to conclude that μ >...
Consider the following hypothesis test. H0: μ ≤ 25 Ha: μ > 25 A sample of...
Consider the following hypothesis test. H0: μ ≤ 25 Ha: μ > 25 A sample of 40 provided a sample mean of 26.4. The population standard deviation is 6. (a) Find the value of the test statistic. (Round your answer to two decimal places.) (b) Find the p-value. (Round your answer to four decimal places.) p-value = (c) At α = 0.01, state your conclusion. Reject H0. There is sufficient evidence to conclude that μ > 25.Reject H0. There is...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT