Saturday, November 19, 2011

1. State the Null Hypothesis and Alternative Hypothesis, 2. Determine the test statistic?

3. Determine the P-value, 4. Make a decision about the hypothesis





Q: According to the National Institute for Occupational Safety and Health, job stress poses a major threat to the health of workers. A national survey of restaurant employees found that 75% said that job stress had a negative mpact on their personal lives. A sample of 100 employees of a restaurant chain finds that 68 answer "Yes" when asked: "Does job stress have a negative impact on your personal life?" Is this good reaon to think that the proportion of all employees of this chain who would say "Yes" differs from the national proportion, p(0)=.75? Use a 5% level of significance.

1. State the Null Hypothesis and Alternative Hypothesis, 2. Determine the test statistic?
1. because the question says "differs" you have a two tail test





H0: p = 0.70 vs H1: p ≠ 0.70





2. Because of the large sample size we can assume normality and use the Z statistic for the hypothesis test





3. the p-value is the probability of observing a sample in bigger disagreement with the null hypothesis H0, than we saw in this case.





Find the test statistic





Z = (p - p0) / Sqrt[p0 * (1-p0) / n]


Z = 0.68 - 0.75 / Sqrt[ 0.7*0.3/100]


Z = -1.5275252





the p-value = P[ Z %26lt; -1.53] + P[ Z %26gt; 1.53] = 0.063 + 0.063 = 0.126





4. since the p-value = 0.126 is greater than the significance level we conclude that H0, the null hypothesis, is plausible. Note that we cannot conclude that the null if true, only that it is plausible.
Reply:Use Normal Distribution


np=u, var=npq


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