Question

PLEASE HELP AND SHOW WORK.... AMD IF THERE IS A CALCULATOR WAY PLEASE SHOW IT ON TI84.

You wish to test the following claim (Ha) at a significance level of α-0.02 Ho: μ = 52.4 52.4 Ha: μ You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n 20 with mean M 55.8 and a standard deviation of SD 6.3. What is the p-value for this sample? (Report answer accurate to four decimal places.) p-value The p-value is... O less than (or equal to) a greater than a This p-value leads to a decision to... Oreject the null Caccept the null Ofail to reject the null As such, the final conclusion is that... °There is sufficient evidence to warrant rejection of the claim that the population mean is not equal to 52.4 There is not sufficient evidence to warrant rejection of the claim that the population mean is not equal to 52.4 mean is not equal to 52.4 claim that the population mean is not equal to 52.4. OThe sample data support the claim that the population ○There is not sufficient sample evidence to support the

Answer 1

Solution:

t-test for testing population mean( $\mu$ ) using p-value method

Given the hypothesis

H0: $\mu$ = 52.4 ....null hypothesis

H1: $\mu$    $\neq$ 52.4 ....alternative hypothesis

n = 20 ....sample size

M = 55.8 ...sample mean

SD= 6.3 ....Sample standard deviation

$\alpha$ = 0.02 .... level of significance

Since population SD is unknown,we use t test.

The test statistics t is given by ..

t = $\frac{M - \mu}{SD/\sqrt{n}}$

= (55.8-52.4)/(6.3/root20)

= 2.4135

Now,n=20 implies ,degrees of freedom =d.f.= n-1 = 20-1 = 19

We want to find p value.We can perform t test using TI-84 calculator. (See the image below)

Our alternative is H1: $\mu$    $\neq$ 52.4  

$\neq$ sign implies that test is two sided test.

using t=2.4135 and d.f.=19 ,two sided test

p-value =0.0260

So, p value is grater than $\alpha$ .

In this case , we fail to reject the null hypothesis.

i.e. we fail to reject H0: $\mu$ = 52.4

As such , the final conclusion is

There is not sufficient sample evidence to support the claim that the population mean is not equal to 52.4

(To see TI-84 command for t test see the image below)