Question

Is college worth it? Among a simple random sample of 331 American adults who do not have a four-year college degree and are not currently enrolled in school, 131 said they decided not to go to college because they could not afford school.

NOTE: While performing the calculations, do not used rounded values. For instance, when calculating a p-value from a test statistic, do not use a rounded value of the test statistic to calculate the p-value. Preserve all the decimal places at each step.

Enter at least 4 decimal places for each answer in WeBWorK.

1. A newspaper article states that only a minority of the Americans who decide not to go to college do so because they cannot afford it and uses the point estimate from this survey as evidence. What are the correct hypotheses for conducting a hypothesis test to determine if these data provide strong evidence supporting this statement?

A. ?0:?=0.5H0:p=0.5, ??:?>0.5HA:p>0.5
B. ?0:?=0.5H0:p=0.5, ??:?<0.5HA:p<0.5
C. ?0:?=0.5H0:p=0.5, ??:?≠0.5HA:p≠0.5

2. Calculate the test statistic for this hypothesis test.  ? z t X^2 F  =

3. Calculate the p-value for this hypothesis test.

4. Based on the p-value, we have:
A. some evidence
B. extremely strong evidence
C. little evidence
D. very strong evidence
E. strong evidence
that the null model is not a good fit for our observed data.

Answer 1

1)

Answer: B.

Explanation: A newspaper article claimed that only a minority of the Americans who decide not to go to college because they cannot afford it which means the claimed proportion is less than 0.50. Hence the null hypothesis is defined as the proportion is 0.50 while the alternative hypothesis tests the claim that this proportion is less than 0.50

2)

Answer: Z = -3.7926

Explanation: To test whether there is a significant difference in results from the survey, the z test for the one proportion is used.

The z-statistic is obtained using the formula,

where, the hypothesized proportion, p0 = 0.50, the sample proportion, p = 131/331 = 0.3958

3)

Answer: P-value = 0.0001

Explanation: The p-value is obtained from the z-distribution table for z = -3.7926

4)

Answer: Based on the p-value, we have: E. strong evidence that the null model is not a good fit for our observed data.

Explanation: Since the p-value is less than 0.05, the null hypothesis is rejected hence conclude that there is strong evidence that the proportion is less than 0.05