Question

--------A sample of 36 observations is selected from a normal population. The sample mean is 34, and the population standard deviation is 5. Carry out a hypothesis test (with a level of significance α of 0.05) of the null hypothesis H0: µ ≥ 35 using the 6-step procedure

---------Suppose that someone claims that the mean number of sick days taken by U.S. employees is 5.1. You decide to investigate that claim and take a representative sample of 87 U.S. employees and find that the mean number of sick days is 4.8 in the sample. The population standard deviation is 1.6. Carry out a hypothesis test (with a level of significance α of 0.05) using the p-value method.

---------Consider the following information: A hypothesis test for a population mean is carried out with a significance level of 0.05. Using the 6-step procedure, the decision is not to reject H0. >>>>>>>Is it possible that the sample value of the test statistic for this test is 0.046? Why or why not?

>>>>>>>>Is it possible that the p-value for this test is 0.046? Why or why not?

Answer 1

Here it is given that the null hypothesis H0: µ ≥ 35

So

Here it is given that the null hypothesis H0: mu greaterthanorequalto So 35 H_1: mu < 35 Now as population standard deviation is know, test statistics is z = x bar - mu/sigma/squareroot n = 34 - 36/5/6 = -2.4 Now P value is P(z < - 2.4) = 0.0082 Here P value is < alpha = 0.05, hence we reject the null hypothesis So we have sufficient evidence to support the claim in alternative hypothesis

Now as population standard deviation is know, test statistics is

Now P value is

Here P value is < $\alpha=0.05$ , hence we reject the null hypothesis

So we have sufficient evidence to support the claim in alternative hypothesis