Question

# 6. Use the pulse rates in beats per minute​ (bpm) of a random sample of adult...

6.

Use the pulse rates in beats per minute​ (bpm) of a random sample of adult females listed in the data set available below to test the claim that the mean is less than 78 bpm. Use a 0.10 significance level.

 Pulse Rate​ (bpm) 102 102 36 100 72 52 46 71 83 87 50 58 36 46 52 94 39 65 40 101 76 65 89 67 99 51 70 44 76 77 57 102 87 79 41 95 82 61 52 84 45 75 68 81 48 101 88 93 105 83

____________________

Assuming all conditions for conducting a hypothesis test are​ met, what are the null and alternative​ hypotheses?

A.

H0​:

μ=78

bpm

H1​:

μ>78

bpm

B.

H0​:

μ=78

bpm

H1​:

μ<78

bpm

C.

H0​:

μ>78

bpm

H1​:

μ<78

bpm

D.

H0​:

μ=78

bpm

H1​:

μ≠78

bpm

______________________

Determine the test statistic. (Round to two decimal places as​ needed.)

Determine the​ P-value. ​(Round to three decimal places as​ needed.)

State the final conclusion that addresses the original claim.

Fail to reject

Reject

H0.

There is

not sufficient

sufficient

evidence to conclude that the mean of the population of pulse rates for adult females is

greater than

less than

not

78

bpm.

for Hypothesis: option B is correct

 null hypothesis: HO: μ = 78 Alternate Hypothesis: Ha: μ < 78
 population mean μ= 78 sample mean 'x̄= 71.46 sample size    n= 50 std deviation s= 21.198 std error ='sx=s/√n=21.1980072224745/√50= 2.9979 t statistic ='(x̄-μ)/sx=(71.46-78)/2.998= -2.18
 p value      = 0.017 from excel: tdist(2.182,49,1)

Reject Ho ; There is sufficient evidence to conclude that the mean of the population of pulse rates for adult females is less than 78 bpm.