Question

# 7. A simple random sample of 43 adults is obtained from a normally distributed​ population, and...

7. A simple random sample of 43 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 5.27 and the sample standard deviation is 0.52. 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

µ< 5.4

t= -1.639359631

p=0.0543043057

x=5.27

Sx=0.52

N=43

What are the null and alternative​ hypotheses?

A.H 0​: µ < 5.4

H 1​: µ = 5.4

B.H 0​: µ =5.4

H 1​: µ < 5.4

C. H 0​: µ = 5.4

H 1​: µ >5.4

D.H 0​: µ = 5.4

H 1​: µ ≠ 5.4

Identify the test statistic.___

​(Round to three decimal places as​ needed.)

Identify the​ P-value._____

​(Round to four decimal places as​ needed.)

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

A.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.

B.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.

C.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.

D.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.

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 comma so it is unlikely 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 unlikely that the population has counts that are too high.

C.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.

D.There is not 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.

To Test :-

B.H 0​: µ =5.4

H 1​: µ < 5.4

Test Statistic :-  t = -1.6394

Test Criteria :-
Reject null hypothesis if   Result :- Fail to reject null hypothesis

Decision based on P value
P - value = P ( t > 1.6394 ) = 0.0543
Reject null hypothesis if P value < level of significance
P - value = 0.0543 > 0.01 ,hence we fail to reject null hypothesis
Conclusion :- Fail to reject null hypothesis

D.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.

D.There is not 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.

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