Question

A. IQ tests are designed so that the mean is 100 points and the standard deviation is 15 points for the entire adult population. What is the minimum sample size needed to estimate the average IQ of all Stat 200 students to within 2 points with 90% confidence?

B. The following data represents the number of days a random sample of patients spent in the hospital after being admitted with a dangerous virus.

22

18

20

19

21

18

22

17

17

23

Assuming that the number of days in the hospital is normally distributed, find a 95% confidence interval for the population mean based on this sample. Give the endpoints of your interval to three decimal places.

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Answer 1

Part a

The sample size formula is given as below:

n = (Z*σ/E)^2

We are given

Confidence level = 90%

Critical Z value = 1.6449

(by using z-table)

σ = 15

E = 2

n = (1.6449*15/2)^2

n = 152.1954

Required sample size = 153

Part b

Confidence interval for Population mean is given as below:

Confidence interval = Xbar ± t*S/sqrt(n)

From given data, we have

Xbar = 19.7

S = 2.213594362

n = 10

df = n - 1 = 9

Confidence level = 95%

Critical t value = 2.2622

(by using t-table)

Confidence interval = Xbar ± t*S/sqrt(n)

Confidence interval = 19.7 ± 2.2622*2.213594362/sqrt(10)

Confidence interval = 19.7 ± 1.5835

Lower limit = 19.7 - 1.5835 = 18.116

Upper limit = 19.7 + 1.5835 = 21.284

Confidence interval = (18.116, 21.284)