Question

(20 points) A statistics practitioner calculated the mean and the standard deviation from a sample of 400. They are x = 98 and s = 20: (a) Compute the p-value in order to test H0 : = 100 against H1 : 6= 100: (b) Compute the p-value in order to test H0 : = 100 against H1 : > 100:

Answer 1

The P-value is 0.0234.

Explanation:

We are given that a statistics practitioner calculated the mean and the standard deviation from a sample of 400. They are x = 98 and s = 20.

Let
`\mu` = population mean.

So, Null Hypothesis,
`H_0` :
`\mu` = 100 {means that the population mean is equal to 100}

Alternate Hypothesis,
`H_A` :
`\mu` > 100 {means that the population mean is more than 100}

The test statistics that will be used here is One-sample t-test statistics because we don't know about population standard deviation;

T.S. =
`(\bar X-\mu)/((s)/(√(n) ) )` ~
`t_n_-_1`

where,
`\bar X` = sample mean = 98

s = sample standard deviation = 20

n = sample size = 400

So, the test statistics =
`(98-100)/((20)/(√(400) ) )` ~
`t_3_9_9`

= -2

The value of t-test statistics is -2.

Now, the P-value of the test statistics is given by;

P(
`t_3_9_9` < -2) = 0.0234 {using the t-table}