Question

To estimate the population mean repair cost of microwave ovens in Macomb, a random sample of 9 broken microwave ovens was selected and it is found that the sample mean repair cost is $80 with a sample standard deviation of $15. Answer the following questions:

1) What would be the critical value if you want to find 90 % confidence interval for the population mean?

2) What would be the margin of error if you want to find 90 % confidence interval for the population mean?

3) What would be the length of the 90 % confidence interval?

4) What would happen to 90 % confidence interval if we decrease the sample size from 9-6? Wider or narrower?

Please show how you answered each. Thank you

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 80

sample standard deviation = s = 15

sample size = n = 9

Degrees of freedom = df = n - 1 = 9-1 = 8

1) At 90% confidence level

= 1-0.90% =1-0.9 =0.10

/2 =0.10/ 2= 0.05

t/2,df = t_{0.05,8 = 1.86}

t _/2,df = 1.86

critical value = 1.86

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

= 1.86 * (15 / 9)

Margin of error = E = 9.3

3) The 90% confidence interval estimate of the population mean is,

- E < < + E

80 -9.3 < < 80+9.3

71.3 < < 89.3

The length of the 90 % confidence interval = (71.3,89.3)

4) Wider