Question

From a random sample of 41 teens, it is found that on average they spend 31.8 hours each week online with a standard deviation of 3.65 hours. What is the 90% confidence interval for the amount of time they spend online each week?

(30.86, 32.74)

(28.15, 35.45)

(29.99, 33.61)

(24.50, 39.10)

A company making refrigerators strives for the internal temperature to have a mean of 37.5 degrees with a standard deviation of 0.6 degrees, based on samples of 100. A sample of 100 refrigerators have an average temperature of 37.70 degrees. Are the refrigerators within the 90% confidence interval?

Yes, the temperature is within the confidence interval of (37.40, 37.60)

No, the temperature is outside the confidence interval of (36.90, 38.10)

Yes, the temperature is within the confidence interval of (36.90, 38.10)

No, the temperature is outside the confidence interval of (37.40, 37.60)

Answer 1

Solution:-

1) 90% confidence interval for the amount of time they spend online each week is C.I = (30.86, 32.74).

Mean = 31.8, S.D = 3.65

C.I = 31.8 + 1.645 × 0.57003

C.I = 31.8 + 0.9377

C.I = (30.840, 32.738)

2) 90% confidence interval for the amount of time they spend online each week is C.I = (37.40, 37.60).

No, the temperature is outside the confidence interval of (37.40, 37.60)

Mean = 37.5, S.D = 0.60, n = 100

C.I = 37.5 + 1.645 × 0.06

C.I = 37.5 + 0.0987

C.I = (37.401, 37.599)