Surveys done at Central and North Seattle. Colleges found that 60% of cell phone

ID: 3132195 • Letter: S

Question

Surveys done at Central and North Seattle. Colleges found that 60% of cell phone calls were not answered and were sent to voice mail. At South, we surveyed 400 students and found that 220 of them had thier last phone call go to voice mail. Construct a test to see if the percentage at South is different from the other colleges. Use a level of significance of 5%.

A) State the null and alternative hypotheses. H0:___ Ha:____

B) What is Zcrit?____

C) What is Zdata?____

D) Do you reject the null hypothesis? Yes___ No___

E) State your conclusion using the words in the problem.

F) What is the p-value associated with this test?

Explanation / Answer

One sample z test for proportion

Surveys done at Central and North Seattle

Colleges found that 60% of cell phone calls were not answered and were sent to voice mail. At South, we surveyed 400 students and found that 220 of them had their last phone call go to voice mail. Construct a test to see if the percentage at South is different from the other colleges. Use a level of significance of 5%.

Solution:

Here, we have to one sample z test for the population proportion. The test is given as below:

Null hypothesis: H0: p = 0.6 versus Alternative hypothesis: Ha: p 0.6

Z – Critical value = 1.96

Test statistic value Z = -2.0412

Yes, we reject the null hypothesis.

We reject the null hypothesis that the population proportion of cell phone calls were not answered and were sent to voice mail is 60% at Central and North Seattle. This means we concluded that the population proportion of cell phone calls were not answered and were sent to voice mail is not 60% at Central and North Seattle.

P-value = 0.0412

Z Test of Hypothesis for the Proportion

Data

Null Hypothesis p =

0.6

Level of Significance

0.05

Number of Items of Interest

220

Sample Size

400

Intermediate Calculations

Sample Proportion

0.55

Standard Error

0.0245

Z Test Statistic

-2.0412

Two-Tail Test

Lower Critical Value

-1.9600

Upper Critical Value

1.9600

p-Value

0.0412

Reject the null hypothesis