Question

Please assist with 6.52 Whats Wrong questions!!! Please explain why, if possible. Thank you!!!

SECTION 6.2 SUMMARY e A test of significance i A test of significance is intended to assess the evidence provide against a null hypothesis Ho in favor of an alternative hypothesis Ha . The hypotheses are stated in terms of population is a statement that no effect or no difference is present, and Ha says there is an effect or difference in a specific direction (one-sided a or in either direction (two-sided alternative). by data parameters. Usually, Ho that lternative) he test is based on a test statistic. The P-value is the probability, computed assuming that Ho is true, that the test statistic will take a value at least as extreme as that actually observed. Small P-values indicate strong evidence against Ho. Calculating P-values requires knowledge of the sampling distribution of the test statistic when Ho is true. If the P-value is as small or smaller than a specified value α, the data are statistically significant at significance level α. . Significance tests for the hypothesis Ho: μ 40 concerning the unknown mean u of a population are based on the z statistic: 0. The z test assumes an SRS of size n, known population standard deviation o, and either a Normal population or a large sample. P-values are compute from the Normal distribution (Table A). Fixed a tests use the table of standard Normal critical values (Table D).

Answer 1

(a) A researcher tests the following null hypothesis :

The null hypothesis (denoted by $H_{0}$ ) is a statement that the value of a population parameter (such as proportion, mean, or standard deviation) is equal to some claimed value.

​It makes no sense to state the sample mean in the hypothesis, as this does not give us any information about the population. The hypotheses should be about the population. When we do the test we only observe the sample, and see whether the data is consistent with the hypothesis. We will never know for sure whether the hypotheses is true or not. ​Thus the null hypothesis should be the assumption about the popualtion parameter. And the alternative hypothesis is not given too.

(b) A random sample of size 30 is taken from the population that is assumed to have a standard deviation of 5. The standard deviation of sample mean is 5/30:

The standard deviation of sample mean 5/30 is wrong.

Given the sample size $(n)=30$ ​ and population standard deviation $(\sigma )=5$

The standard error of the mean is the standard deviation of the sampling distribution of the mean. Thus the formula for standard deviation of sample mean is,

   $\sigma _{M}=(\sigma )/(n)^{1/2}$

   $=5/(30)^{1/2}$

$\sigma _{M}=0.913$

Thus the standard deviation of sample mean is $5/(30)^{1/2}$ and not .

(c) A study with $x_{bar}=45$ ​ reports statistical significance for $H_{a}:\mu >50$ :

A study with $x_{bar}=45$ ​ ​would not make us inclined to believe that $\mu >50$ . Because we will always conclude with respect to null hypothesis $H_{0}$ ​ which is not stated in the given situation.

(d) A researcher tests the hypothesis $H_{0}:\mu =350$ and concludes that the population mean is equal to 350:

The null hypothesis (denoted by $H_{0}$ ) is a statement that the value of a population parameter (such as proportion, mean, or standard deviation) is equal to some claimed value.

We always test the null hypothesis.

The initial conclusion will always be one of the following:

1. Reject the null hypothesis.

2. Fail to reject the null hypothesis.

Even if we fail to reject the null hypothesis, we are not sure that it is true. That is "not rejecting $H_{0}$ ​" is different from "Knowing that $H_{0}$ ​ is true". It is simply that there is no sufficient evidence to prove that $H_{0}$ ​ is false.

Thus we wont conclude that the population mean is equal to 350 as we are not sure that it is true. Rather we conclude that there is no sufficient evidence to prove that $H_{0}:\mu =350$ ​ is false.