Question

1. From a sample of 37 stolen watches, you find that the mean cash value is $950. The standard deviation for your sample is $90. Test the null hypothesis that your sample came from a population whose mean cash value (Mu) is $1,000 against the alternative hypothesis that Mu is different than $1,000. Use alpha = .05.

a. Formally state the alternative and the null hypothesis for this test

b. What is the critical value(s) for this test?

c. Compute and report the test statistic.

d. Interpret your decision regarding the null hypothesis

e. If necessary, compute 95% confidence intervals for the population mean and interpret.

Answer 1

Answer)

A)

Null hypothesis Ho : u = 1000

Alternate hypothesis Ha : u not equal to 1000

B)

As the population s.d is unknown here we will use t distribution to estimate the critical value

Degrees of freedom = n-1 = 37-1 = 36

For 36 df and 0.05 alpha

Critical values from t table are = -2.028 and 2.028

Rejection region is

Reject Ho if test statistics is < -2.028 or > 2.028

C)

Test statistics t = (sample mean - claimed mean)/(s.d/√n)

t = (950 - 1000)/(90/√37) = -3.379

D)

As -3.379 < -2.028

We reject the. Null hypothesis Ho

E)

For df 36 and 95% confidence level critical value t = 2.028

Margin of error (MOE) = t*s.d/√n = 2.028*90/√37 = 30.0061031629

Confidence interval is given by

(Mean - MOE, Mean + MOE)

[919.99, 980.01].

As the interval do not have 1000 (null hypothesised value)

We reject the null hypothesis Ho.