Question

**Steps to be covered:**

**state the hypothesis and identify the claim****find the critical value from the table and mention the acceptance range for H0****compute the test value****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)

1.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 2.A college wants to know the lower limit of a two-sided
80% confidence interval for SAT scores on the Math section (range
equals 200 to 800). They...

A Rollercoaster’s auditors estimate that the average daily loss
from those illegally riding without tickets is at least (greater or
equal) $250, but wants to determine the accuracy of this statistic.
The company researcher takes a random sample of losses over 81 days
and finds that = $248 and s = $15. a) Test at α = 0.02. b)
Construct a 90% confidence interval of losses Note: a and b are
independent.
Steps to be covered:
state the hypothesis and...

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