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 |

s^{2}= |
0.384 |

Critical value of chi square distribution for n-1=96 df and 95 % CI | ||||

Lower critical value χ^{2}_{L}= |
70.783 |
from excel: chiinv(0.975,96) |
||

Upper critical valueχ^{2}_{U}= |
125.000 |
from excel: chiinv(0.025,96) |

for Confidence interval of standard deviation: | |

Lower
bound
=√((n-1)s^{2}/χ^{2}_{U})= |
0.543 |

Upper
bound
=√((n-1)s^{2}/χ^{2}_{L})= |
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.

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