Question

A publisher reports that 48% of their readers own a personal computer. A marketing executive wants to test the claim that the percentage is actually under the reported percentage. A random sample of 400 found that 45% of the readers owned a personal computer. Is there sufficient evidence at the 0.05 level to support the executive's claim?

Step 1 of 7:  State the null and alternative hypotheses.

Step 2 of 7: Find the value of the test statistic. Round your answer to two decimal places.

Step 3 of 7: Find the p-value.

Step 4 of 7: What is the level of significance

Step 5 of 7: Is this one-tailed or two-tailed

Step 6 of 7: Make a decision to reject or fail to reject

Step 7 of 7:  Is there enough evidence at the 0.05 level to support the officer's claim

GET ALL CORRECT FOR A THUMBS UP!  

Answer 1

Solution:

Given:

Given:

Sample size = n = 400

Sample proportion = = 0.45

1)Null and alternative hypothesis:

2)Test statistic:

Test statistic z = -1.20

3)Using the P-value approach:

P(Z<0-1.201) = 0.1149 …Using excel function, =NORMSDIST(-1.20)

The p-value is p = 0.1149

4)And α = 0.05

5)This corresponding to a one-tailed test, for which a z-test for one population proportion needs to be used.

6)Decision: Since p = 0.1149 >0.05, it is concluded that the Null Hypothesis is not rejected.

7)Conclusion: Therefore, there is not enough evidence to support the claim that percentage is actually under the reported percentage.

Done