Question

A simple random sample of 44 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 5.25 and the sample standard deviation is 0.55. 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 comma 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? ? T-Test ??muless than5.4 ??tequalsnegative 1.809068067 ??pequals0.0387176309 ??x overbarequals5.25 ??Sxequals0.55 ??nequals44 What are the null and alternative? hypotheses? A. Upper H 0?: muequals5.4 Upper H 1?: muless than5.4 B. Upper H 0?: muless than5.4 Upper H 1?: muequals5.4 C. Upper H 0?: muequals5.4 Upper H 1?: mugreater than5.4 D. Upper H 0?: muequals5.4 Upper H 1?: munot equals5.4 Identify the test statistic. nothing ?(Round to three decimal places as? needed.) Identify the? P-value. nothing ?(Round to four decimal places as? needed.) State the final conclusion that addresses the original claim. Choose the correct answer below. A. Fail to reject Upper H 0. 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 Upper H 0. There is sufficient evidence to support the claim that the sample is from a population with a mean less than 5.4. C. Reject Upper H 0. There is not sufficient evidence to support the claim that the sample is from a population with a mean less than 5.4. D. Reject Upper H 0. There is 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 comma 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 comma so it is unlikely that the population has counts that are too high. .

Answer 1

H₀: = 5.4

H₁: < 5.4

The test statistic t = ()/(s/)

                             = (5.25 - 5.4)/(0.55/)

                             = -1.81

DF = 44 - 1 = 43

P-value = P(T < -1.81)

             = 0.0386

As the P-value is greater than the significance level (0.0386 > 0.01), we should not reject H₀.

Option - A) 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

Option - 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.2