a newspaper headline claims that less 70% of workers get their jobs through netw

Question

a newspaper headline claims that less 70% of workers get their jobs through networking. a random sample of 300 recent college students were contacted. sixty seven percent said they got their job through networking. was the newspapers claim accurate? ( test at .05 level of significance)

a) state null and altnerative
b) state formula used and show work
c) do you reject of fail to reject null. why
d) was the newspapers claim accurate

Explanation / Answer

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 < -1.53] + P[ Z > 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, b)do you reject of fail to reject null If the p-value of the test is less than or equal to the significance level a, i.e., p-value = a, then we reject the null hypothesis and conclude the alternate hypothesis is true. If the p-value is greater than the significance level, i.e., p-value > a, then we fail to reject the null hypothesis and conclude that the null is plausible. Note that we can conclude the alternate is true, but we cannot conclude the null is true, only that it is plausible. Consider the hypothesis as a trial against the null hypothesis. the data is evidence against the mean. you assume the mean is true and try to prove that it is not true. After finding the test statistic and p-value, if the p-value is less than or equal to the significance level of the test we reject the null and conclude the alternate hypothesis is true. If the p-value is greater than the significance level then we fail to reject the null hypothesis and conclude it is plausible. Note that we cannot conclude the null hypothesis is true, just that it is plausible. If the question statement asks you to determine if there is a difference between the statistic and a value, then you have a two tail test, the null hypothesis, for example, would be µ = d vs the alternate hypothesis µ ? d if the question ask to test for an inequality you make sure that your results will be worth while. for example. say you have a steel bar that will be used in a construction project. if the bar can support a load of 100,000 psi then you'll use the bar, if it cannot then you will not use the bar. if the null was µ = 100,000 vs the alternate µ < 100,000 then will will have a meaningless test. in this case if you reject the null hypothesis you will conclude that the alternate hypothesis is true and the mean load the bar can support is less than 100,000 psi and you will not be able to use the bar. However, if you fail to reject the null then you will conclude it is plausible the mean is greater than or equal to 100,000. You cannot ever conclude that the null is true. as a result you should not use the bar because you do not have proof that the mean strength is high enough. if the null was µ = 100,000 vs. the alternate µ > 100,000 and you reject the null then you conclude the alternate is true and the bar is strong enough; if you fail to reject it is plausible the bar is not strong enough, so you don't use it. in this case you have a meaningful result. Any time you are defining the hypothesis test you need to consider whether or not the results will be meaningful.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.