Quiz: Final Exam Time This Question: 14 pts This Quiz: 250 pts One study, based
ID: 3296956 • Letter: Q
Question
Quiz: Final Exam Time This Question: 14 pts This Quiz: 250 pts One study, based on responses from 1,016 randomly selected feel that grades are their greatest source of pressure Formulate the null and atemative hypoteses Choose the correct answer below H, p 05 H, p.05 H, p-05 State the conclusion. Choose the correct answer belowr O A. Reject Ho. There is sufficient evidence to support the claim that fewer than half of all teenagers in the papulation feel that grades are the greatest source of pressure B. Do not reect He. There is sufficiant evidence to suceot the claim that fower than half of all teenaoers in the copulation Seel that arades are the areatest sounce of oressure Click to select your answers) Type hete to sear /23/2017Explanation / Answer
Solution:-
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: P > 0.50
Alternative hypothesis: P < 0.50
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 ]
= 0.01569
z = (p - P) /
z = - 5.74
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 - 5.74. We use the Normal Distribution Calculator to find P(z < - 5.74) = 0.0001.
Thus, the P-value = 0.0001
Interpret results. Since the P-value (0.0001) is less than the significance level (0.05), we cannot accept the null hypothesis.
Reject H0, there is sufficient evidence to supprt the claim that lower than half of all teenagers in the population feels that grade are the greatest source of pressure.
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