Can someone help me figure out how to solve this? According to a Gallup survey c

Question

Can someone help me figure out how to solve this?

According to a Gallup survey conducted in July 2011, 20% of adults in the U.S. favor reducing the U.S. budget deficit by using spending cuts only, with no tax increases. An economics professor believes that fewer college students would favor deficit reduction through spending cuts only.

The professor surveys 500 college students and finds that 75 of them favor reducing the deficit using only spending cuts. What is the test statistic?

Round your standard error to three decimal places and your test statistic to two decimal places.

Explanation / Answer

Solution:-

x = 75, n = 500

p = 75/500

p = 0.15

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: P > 0.20

Alternative hypothesis: P < 0.20

Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected only if the sample proportion is too small.

Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method, shown in the next section, is a one-sample z-test.

Analyze sample data. Using sample data, we calculate the standard deviation () and compute the z-score test statistic (z).

= sqrt[ P * ( 1 - P ) / n ]

= 0.0179

z = (p - P) /

z = - 2.79

where P is the hypothesized value of population proportion in the null hypothesis, p is the sample proportion, and n is the sample size.

Since we have a one-tailed test, the P-value is the probability that the z-score is less than - 2.79. We use the Normal Distribution Calculator to find P(z < - 2.79) = 0.0026

Interpret results. Since the P-value (0.0026) is less than the significance level (0.05), we cannot accept the null hypothesis.

From the above test we have sufficient evidence in the favor of the claim that fewer college students would favor deficit reduction through spending cuts only.

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