Question

One study claimed that 89% of college students identify themselves as procrastinators. A professor believes that the claim regarding college students is too high. The professor conducts a simple random sample of 184 college students and finds that 157 of them identify themselves as procrastinators. Does this evidence support the professor’s claim that fewer than 89% of college students are procrastinators? Use a 0.02 level of significance.

Step 1 of 3:

State the null and alternative hypotheses for the test. Fill in the blank below.


H0: p=0.89

Ha: p⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯0.89

Step 2 of 3:

Compute the value of the test statistic. Round your answer to two decimal places.

Step 3 of 3:

Draw a conclusion and interpret the decision.

Answer 1

The evidence supports the professor's claim that fewer than 89% of college students are procrastinators.

Step-by-step explanation:

To test whether the evidence supports the professor's claim, we need to conduct a hypothesis test. The null hypothesis, denoted as H0, assumes that the proportion of college students who identify as procrastinators is equal to 89%. The alternative hypothesis, denoted as Ha, assumes that the proportion is less than 89%. In this case, the hypotheses can be written as:

H0: p = 0.89
Ha: p < 0.89

Next, we compute the test statistic. For this, we use the formula for a test statistic for proportions:

test statistic = (p-hat - p) / sqrt((p * (1-p) / n)

where p-hat is the sample proportion, p is the hypothesized proportion under the null hypothesis, and n is the sample size. Plugging in the values, we get:

p-hat = 157/184 ≈ 0.853

test statistic = (0.853 - 0.89) / sqrt((0.89 * (1-0.89) / 184) ≈ -2.19

Finally, we compare the test statistic to critical values from the standard normal distribution at a significance level of 0.02. If the test statistic is less than the critical value, we reject the null hypothesis. In this case, the critical value is approximately -2.17. Since the test statistic (-2.19) is less than the critical value (-2.17), we reject the null hypothesis. This means that there is sufficient evidence to support the professor's claim that fewer than 89% of college students are procrastinators.