Question

HYPOTHEIS TESTING [THINKING AHEAD!!!]. An economist reports that 558 out of a sample of 1,200 middle-income American households actively participate in the stock market. Can we conclude that the proportion of middle-income Americans that actively participate in the stock market is NOT 50%? Test at the 5% level of significance.

		REJECT THE NULL HYPOTHESIS. The calculate Z value is -2.425. YES, we can conclude that the proportion of middle-income Americans participating in the stock market is NOT 50%.
		DO REJECT THE NULL HYPOTHESIS. The calculate Z value is -2.425. We cannot conclude that the proportion of middle-income Americans participating in the stock market is NOT 50%.
		REJECT THE NULL HYPOTHESIS. The calculate p-hat (sample proportion) is 46.5%. Based on this evidence alone, and without further statistical analysis, we can conclude that the proportion of middle-income Americans participating in the stock market is NOT 50%.
		None of the above

Answer 1

Let p denotes the true proportion of middle-income Americans that actively participate in the stock market.

To test against

Here

sample proportion

and sample size

The test statistic can be written as

which under H₀ follows a standard normal distribution.

We reject H₀ at 5% level of significance if P-value < 0.05

Now,

The value of the test statistic

P-value

Since P-value < 0.05, so we reject H₀ at 5% level of significance and we can conclude that the proportion of middle-income Americans that actively participate in the stock market is NOT 50%

ans-> REJECT THE NULL HYPOTHESIS. The calculate Z value is -2.425. YES, we can conclude that the proportion of middle-income Americans participating in the stock market is NOT 50%.