Question

Steps to be covered:

1. state the hypothesis and identify the claim
2. find the critical value from the table and mention the acceptance range for H0
3. compute the test value
4. make the decision to reject or not the null hypothesis

Mall security estimates that the average daily per-store theft is no more than $250, but wants to determine the accuracy of this statistic. The company researcher takes a sample of 64 clerks and finds that =$252 and s = $10.

a) Test at α = .05

b) Construct a 90% CIE of μ

Answer 1

a)

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 250
Alternative Hypothesis, Ha: μ > 250

Rejection Region
This is right tailed test, for α = 0.05 and df = 63
Critical value of t is 1.669.
Hence reject H0 if t > 1.669

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (252 - 250)/(10/sqrt(64))
t = 1.60

fail to reject null hypothesis.

b)

sample mean, xbar = 252
sample standard deviation, s = 10
sample size, n = 64
degrees of freedom, df = n - 1 = 63

Given CI level is 90%, hence α = 1 - 0.9 = 0.1
α/2 = 0.1/2 = 0.05, tc = t(α/2, df) = 1.669

ME = tc * s/sqrt(n)
ME = 1.669 * 10/sqrt(64)
ME = 2.0863

CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))
CI = (252 - 1.669 * 10/sqrt(64) , 252 + 1.669 * 10/sqrt(64))
CI = (249.91 , 254.09)