Question

7. A data set includes 108 body temperatures of healthy adult humans having a mean of 98.3 F° and a standard deviation of 0.69 F°. Construct a 99​% confidence interval estimate of the mean body temperature of all healthy humans. What does the sample suggest about the use of 98.6 F° as the mean body​ temperature?

What is the confidence interval estimate of the population mean µ​?

____F°<µ<____ F°

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

What does this suggest about the use of 98.6 F° as the mean body​ temperature?

A.This suggests that the mean body temperature could be lower than 98.6 F°.

B.This suggests that the mean body temperature could be higher than 98.6 F°

C.This suggests that the mean body temperature could very possibly be 98.6 F°.

8. An IQ test is designed so that the mean is 100 and the standard deviation is 14 for the population of normal adults. Find the sample size necessary to estimate the mean IQ score of statistics students such that it can be said with 95​% confidence that the sample mean is within 7 IQ points of the true mean. Assume that σ= 14 and determine the required sample size using technology. Then determine if this is a reasonable sample size for a real world calculation.

The required sample size is

nothing. ​(Round up to the nearest​ integer.)

Would it be reasonable to sample this number of​ students?

Yes. This number of IQ test scores is a fairly small number.

Yes. This number of IQ test scores is a fairly large number.

No. This number of IQ test scores is a fairly large number.

No. This number of IQ test scores is a fairly small number

Answer 1

Solution :

7) Given that,

Point estimate = sample mean = = 98.3

sample standard deviation = s = 0.69

sample size = n = 108

Degrees of freedom = df = n - 1 = 108 - 1 = 107

At 99% confidence level

= 1 - 99%

=1 - 0.99 =0.01

/2 = 0.005

t/2,df = t_0.005,107 = 2.623

Margin of error = E = t_/2,df * (s /n)

= 2.623 * ( 0.69/ 108)

Margin of error = E = 0.174

The 99% confidence interval estimate of the population mean is,

- E < < + E

98.3 - 0.174 < < 98.3 + 0.174

(98.126 < < 98.474)

correct option is = C

This suggests that the mean body temperature could very possibly 98.6 degrees F.

8) Given that,

Population standard deviation = = 14

Margin of error = E = 7

At 95% confidence level the z is,

= 1 - 95%

= 1 - 0.95 = 0.05

/2 = 0.025

Z_/2 = 1.96

sample size = n = [Z_/2* / E] ²

n = [1.96 *14 / 7]²

n = 15.36

Sample size = n = 16

No. This number of IQ test scores is a fairly small number