Question

Q24.

The quality assurance​ (QA) manager at a large medical clinic is concerned about how long patients have to wait before being admitted to see a doctor. She asks you to use your statistics skills to evaluate the service being provided by the clinic.

The clinic administration claims that patients only have to wait 30 minutes or less before seeing a doctor. The QA manager is worried that the average time is over 30 minutes.

Based upon past​ studies, the population standard deviation of waiting time is known to be 12 minutes.

Over a period of 2​ weeks, you take a random sample of 16 patients and measure how long each had to wait. The average waiting time for the sample is 35 minutes. Is this sufficient evidence to suggest that the mean waiting time is greater than 30​ minutes?

The QA manager at the clinic uses a​ 5% level of significance.  

The critical value for this hypothesis test is​ ______ and the​ test-statistic from the sample data is​ _______.

A.

1.645​ , 0.42

B.

1.645​ , 1.67

C.

1.96 ​ , 1.67

D.

1.96 ​ , 0.42

Q25.

The quality assurance​ (QA) manager at a large medical clinic is concerned about how long patients have to wait before being admitted to see a doctor. She asks you to use your statistics skills to evaluate the service being provided by the clinic.

The clinic administration claims that patients only have to wait 30 minutes or less before seeing a doctor. The QA manager is worried that the average time is over 30 minutes.

Based upon past​ studies, the population standard deviation of waiting time is known to be 12 minutes.

Over a period of 2​ weeks, you take a random sample of 16 patients and measure how long each had to wait. The average waiting time for the sample is 35 minutes. Is this sufficient evidence to suggest that the mean waiting time is greater than 30​ minutes?

The QA manager at the clinic uses a​ 5% level of significance.  

The conclusion to this hypothesis test​ is:

A.

Ah​ Hah! Reject the Null hypothesis

B.

Ho Hum. Insufficient evidence with which to Reject the Null hypothesis

Answer 1

Solution :

= 30

= 35

= 12

n = 16

This is the right tailed test .

The null and alternative hypothesis is

H0 :   = 30

Ha : > 30

= 0.05  

The right tailed test critical value is 1.645

Test statistic = z

= ( - ) / / n

= (35 -30) / 12 / 16

= 1.67

The critical value for this hypothesis test is​ 1.645 and the​ test-statistic from the sample data is​ 1.67

p(Z > 1.67 ) = 1-P (Z < 1.67) = 0.9525

P-value = 0.9525

= 0.05  

0.9525 > 0.05

Do not reject the null hypothesis .

There is insufficient evidence to suggest that