Question

Consider the following hypothesis test:

H ₀:  = 17

H _a:   17

A sample of 40 provided a sample mean of 14.12. The population standard deviation is 4.

a. Compute the value of the test statistic (to 2 decimals). (If answer is negative, use minus “-“ sign.)

b. What is the p-value (to 4 decimals)?

c. Using  = .05, can it be concluded that the population mean is not equal to 17? SelectYesNoItem 3

Answer the next three questions using the critical value approach.

d. Using  = .05, what are the critical values for the test statistic (to 2 decimals)? ±

e. State the rejection rule: Reject H ₀ if z is Selectgreater than or equal togreater thanless than or equal toless thanequal tonot equal toItem 5 the lower critical value and is Selectgreater than or equal togreater thanless than or equal toless thanequal tonot equal toItem 6 the upper critical value.

f. Can it be concluded that the population mean is not equal to 17?
SelectYesNo

Answer 1

a.

Since, we know the population standard deviation, we will use z test statistic (normal distribution).

Standard error of mean = = 4 / = 0.6324555

Test statistic, z = (Observed mean - Hypothesized Mean) / Standard error

= (14.12 - 17) / 0.6324555

= -4.55

b.

For two tail hypothesis (H _a:   17),

p-value = 2 * P(z < -4.55) = 0.0000

c.

Since p-value is less than 0.05 significance level, we reject null hypothesis H0 and conclude that there is significant evidence that that the population mean is not equal to 17.

Yes.

d.

Using  = .05, the critical values for the test statistic z = 1.96

e.

Reject H ₀ if z is less than the lower critical value or greater than the upper critical value.

f.

Since the test statistic is less than -1.96, it can be concluded that mean is not equal to 17.

Yes