Question

A publisher reports that 29% of their readers own a laptop. A marketing executive wants to test the claim that the percentage is actually different from the reported percentage. A random sample of 380 found that 25% of the readers owned a laptop. Find the value of the test statistic. Round your answer to two decimal places.

Answer 1

SOLUTION:

From given data,

A publisher reports that 29% of their readers own a laptop. A marketing executive wants to test the claim that the percentage is actually different from the reported percentage. A random sample of 380 found that 25% of the readers owned a laptop.

Let    be the proportion of readers own a laptop = 0.25

Let n be the random sample = 380.

Null hypothesis: Ho : p= 0.29

Alternative hypothesis, Ha : p   0.29 (two tail test)

Assume the level of significance, = 0.05.

Compute the test statistic:

= -1.71839

Thus , the test statistics is z = -1.718

The p- value of the test statistic is,

p- value = 2 p(Z > |z| )

= 2 p(Z > 1.718 )

= 2[1-p(z <1.718)]

= 2[1-NORMDIST(1.718)]

= 2[1- 0.95710169]

= 2[0.04289831]

= 0.08579

  = 0.08 (Round your answer to two decimal places.)

Since the p-value of the test is greater than the level of significance , do not reject the null hypothesis at 0.05 level of significance.