Question

A simple random sample of 48 adults is obtained from a normally distributed​ population, and each​ person's red blood cell count​ (in cells per​ microliter) is measured. The sample mean is

5.29 and the sample standard deviation is 0.53. Use a 0.01 significance level and the given calculator display to test the claim that the sample is from a population with a mean less than

5.4 which is a value often used for the upper limit of the range of normal values. What do the results suggest about the sample​ group?

State the final conclusion that addresses the original claim. Choose the correct answer below.

A. Reject H0. There is not sufficient evidence to support the claim that the sample is from a population with a mean less than 5.4

B. Fail to reject H0. There is sufficient evidence to support the claim that the sample is from a population with a mean less than 5.4

C. Reject H0. There is sufficient evidence to support the claim that the sample is from a population with a mean less than 5.4

D. Fail to reject H0. There is not sufficient evidence to support the claim that the sample is from a population with a mean less than 5.4

What do the results suggest about the sample group?

A. There is not enough evidence to conclude that the sample is from a population with a mean less than 5.4, so it is possible that the population has counts that are too high.

B. There is enough evidence to conclude that the sample is from a population with a mean less than 5.4, so it is possible that the population has counts that are too high.

C. There is not enough evidence to conclude that the sample is from a population with a mean less than 5.4, so it is unlikely that the population has counts that are too high.

D. There is enough evidence to conclude that the sample is from a population with a mean less than 5.4, so it is unlikely that the population has counts that are too high.

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 5.4
Alternative Hypothesis, Ha: μ < 5.4

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (5.29 - 5.4)/(0.53/sqrt(48))
t = -1.438

P-value Approach
P-value = 0.0785
As P-value >= 0.01, fail to reject null hypothesis.

D. Fail to reject H0. There is not sufficient evidence to support the claim that the sample is from a population with a mean less than 5.4

A. There is not enough evidence to conclude that the sample is from a population with a mean less than 5.4, so it is possible that the population has counts that are too high.