Question

Where do CFOs get their money news? According to Robert Half International, 47% get their money news from newspapers, 15% get it from communication/colleagues, 12% get it from television, 11% from the Internet, 9% from magazines, 5% from radio, and 1% do not know. Suppose a researcher wants to test these results. She randomly samples 76 CFOs and ?nds that 40 of them get their money news from newspapers. Does the test show enough evidence to reject the ?ndings of Robert Half International? Use a = .05. Make sure you clearly state both the null and the alternative hypotheses in full sentences. Following your calculations, clearly state the conclusion in the same manner (do not simply say “accept/reject null”) and explain how you arrived at this conclusion (based on which metrics).

Answer 1

Given Sample size n = 76

40 of them get their money news from newspapers. So x = 40

Step 1: Set up null and alternative hypotheses.

According to Robert Half International, 47% get their money news from newspapers

So our null and alternate hypothesis is as follows:

H₀: p = 0.47

H₁: p ? 0.47

Step 2: Determine level of significance of hypothesis test.

? = 0.05 (Note: ? = level of significance of hypothesis test = probability of making Type I error.)

Step 3: Calculate Test Statistic.

p? = sample proportion = 0.5263 (Note: p? = x/n = 40/76)
n = sample size = 76
Calculate Test Statistic z:
       

z = (0.5263-0.47)/SQRT(0.47*(1-0.47)/76)

z = 0.98

Step 4: Determine P-value

Using the test statistic in Step 3 as a z-score, we will find the left-tailed area and right-tailed area corresponding to this z-score.

Test Statistic = 0.98
Left-tailed area corresponding to z-score of -0.98 = 0.1635
Right-tailed area corresponding to z-score of 0.98 = 0.1635
p-value = Left-Tailed Area + Right-Tailed Area = 0.327

Step 5: Make Decision

p-value = 0.327

? = 0.05

In this case, p-value is greater than ?.

If p-value is greater than ? then do not reject the null hypothesis.

Conclusion:

There is not enough evidence to to reject the ?ndings of Robert Half International at ? = 0.05