Question

The waiting time for customers at MacBurger Restaurants follows a normal distribution with a population standard deviation of 4 minute. At the Warren Road MacBurger, the quality assurance department sampled 75 customers and found that the mean waiting time was 27.25 minutes. At the 0.10 significance level, can we conclude that the mean waiting time is less than 28 minutes? Use α = 0.10.

a. State the null hypothesis and the alternate hypothesis.

H₀: μ ≥           

H₁: μ <           

b. State whether the decision rule is true or false: Reject H₀ if z < -1.282.

(Click to select)  True  False

c. Compute the value of the test statistic. (Negative answer should be indicated by a minus sign. Round the final answer to 2 decimal places.)

Test statistic z is            .

d. What is your decision regarding H₀?

(Click to select)  Reject  Do not reject  H₀.

e. What is the p-value? (Round the final answer to 4 decimal places.)

The p-value is

Answer 1

Solution :

= 28

=27.25

=4

n = 75

a )This is the left tailed test .

The null and alternative hypothesis is ,

H0 :    ≥ 28

Ha : < 28

The critical value = -1.282

Test statistic = z

= ( - ) / / n

= (27.25-28) / 4 / 75

= -1.62

Test statistic = z =  -1.62

b ) The critical value = -1.282

P-value =0.0526

= 0.10

P-value <

0.0526 < 0.10

Reject the null hypothesis .

There is sufficient evidence to suggest that