Question

In: Statistics and Probability

Suppose you are running the bowling alley and are interested in finding the distribution of shoe...

Suppose you are running the bowling alley and are interested in finding the distribution of shoe sizes for women in order to buy a good fitting distribution of shoes. You took a random sample of 36 women and the mean size was an 8 with a standard deviation of 2. Create and interpret an approximate 95% confidence interval, with the appropriate critical T or Z value, for the mean shoe size of all women.

Expert Solution

Solution :

Given that,

= 8

s = 2

n = 36

Degrees of freedom = df = n - 1 = 36 - 1 = 35

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

t_/2,df = t_0.025,35 =2.030

Critical t value = 2.030

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

= 2.030 * ( 2 / $\sqrt$ 36)

= 0.68

Margin of error = 0.68

The 95% confidence interval estimate of the population mean is,

- E < < + E

8 - 0.68 < < 8 + 0.68

7.32 < < 8.68

(7.32 , 8.68)

orchestra answered 1 year ago

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