For the hypothesis test h0: μ = 10 against h1: μ > 10 and variance known, calculate the pvalue for each of the following test statistics.(a) z0 = 2.05 (b) z0 = −1.84 (c) z0 = 0.4

a)

b)

c)

Step-by-step explanation:

Some previous concepts

The p-value is the probability of obtaining the observed results of a test, assuming that the null hypothesis is correct.

A z-test for one mean "is a hypothesis test that attempts to make a claim about the population mean(μ)".

The null hypothesis attempts "to show that no variation exists between variables or that a single variable is no different than its mean"

The alternative hypothesis "is the hypothesis used in hypothesis testing that is contrary to the null hypothesis"

Hypothesis

Null hypothesis:

Alternative hypothesis:

If the random variable is distributed like this:

We assume that the variance is known so the correct test to apply here is the z test to compare means, the statistic is given by the following formula:

Since we have the values for the statistic already calculated we can calculate the p value using the following formulas:

Part a

And in order to find the answer using excel we can use the following code:

"=1-NORM.DIST(2.05,0,1,TRUE)"

Part b

And in order to find the answer using excel we can use the following code:

"=1-NORM.DIST(-1.84,0,1,TRUE)"

Part c

And in order to find the answer using excel we can use the following code:

"=1-NORM.DIST(0.4,0,1,TRUE)"

Conclusions

If we use a reference value for the significance, let's say . For part a the so then we can reject the null hypothesis at this significance level.

For part b the so then we FAIL to reject the null hypothesis at this significance level.

For part c the so again we FAIL to reject the null hypothesis at this significance level.

7.25

step-by-step explanation:

we know that 7 equals to 7.0. we also know that 1/4=0.25. so we can add the two together and we get 7.25