Question

Please type answer, can't see written answers well.

Also PLEASE PROVIDE BELL SHAPED CURVE** That is the part I struggle with the most.

Zingo's Grocery store claims that customers spend an average of 5 minutes waiting for service at the stores deli counter. A random sample of 40 customers was timed at the deli counter, and the average service time was found to be 5.85 minutes. Historically the standard deviation for waiting time is 1.75 minutes per customer.

a. Find the 95% confidence interval for the mean time that customers wait at the deli counter.

b. Is there sufficient evidence to indicate that the mean time that a customer spends waiting at the deli counter is 5 minutes? Use α = .02 significance level .

Answer 1

=5, n=40, = 5.85,  =1.75

A) C= 95%

Formula for confidence interval is

Where Zc is the Z critical value for C=95%

Hence Zc= 1.96

(5.3077< < 6.3923)

Thus we get confidence interval as follows

(5.3077 , 6.3923)

B) = 0.02

Ho: = 5

Ha: 5

Calculate test statistics

Z= 3.0719

Z= 3.07

Calculate P-Value

P-value= 2*1-P(z<3.07)

Find P(z<3.07) using normal z table we get

P(z<3.07) = 0.9989

P-value= 2* 1-0.9989

P-Value =0.0022

Since ( P-value=0.0022) < ( =0.02 )

Hence Reject Ho.

Critical values are = ( -2.33 , 2.33)

From the bell shaped curve we observe that test statistics lies in rejection region hence

Reject Ho.

Therefor there is not sufficient evidence to claim that mean waiting time that customer spend waiting is 5 minute.