Question

1. A simple random sample from a population with a normal distribution of 97 body temperatures has x=98.90°F and s=0.62°F. Construct a 95​% confidence interval estimate of the standard deviation of body temperature of all healthy humans.

?°F.< σ < ?°F

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

2. The test statistic of z=2.45 is obtained when testing the claim that p>0.3.

a. Identify the hypothesis test as being​ two-tailed, left-tailed, or​ right-tailed.

b. Find the​ P-value.

c. Using a significance level of f a=0.05​, should we reject H0 or should we fail to reject H0​?

a. This is a ▼  test.

b. P-value=. ​(Round to three decimal places as​ needed.)

c. Choose the correct conclusion below.

A. Fail to rejectFail to reject H0. There is notis not sufficient evidence to support the claim that p>0.3.

B. Fail to rejectFail to reject H0. There is sufficient evidence to support the claim that p>0.3.

C. RejectReject Upper H0. There is notis not sufficient evidence to support the claim that p>0.3.

D. RejectReject H0. There Is sufficient evidence to support the claim that p>0.3.

Answer 1

1)

here n =	97
s2=	0.384

Critical value of chi square distribution for n-1=96 df and 95 % CI
Lower critical value χ2L=		70.783		from excel: chiinv(0.975,96)
Upper critical valueχ2U=		125.000		from excel: chiinv(0.025,96)

for Confidence interval of standard deviation:
Lower bound =√((n-1)s2/χ2U)=	0.543
Upper bound =√((n-1)s2/χ2L)=	0.722

from above 95% confidence interval for population standard deviation =(0.54<σ<0.72)

2)

a) since we are checking if proportion is greater than 0.3

this is a right tailed test

b)

p value from excel: =1-normsdist(2.45)=0.007

c)

since p value <0.05 ; option D is correct

Reject H0. There Is sufficient evidence to support the claim that p>0.3.