Question

Consider the following hypotheses: H0: mean = 5 H1: mean < 5 A test is performed with a sample of size 25. The sample mean was 4.73 and the population standard deviation is 1.2. Assume that the population is approximately normal. Use the TI-84 PLUS calculator to compute the P-value. Round your answer to four decimal places (for example: 0.0138). Write only a number as your answer.

Answer 1

0.1406.

Explanation:

Given :
`H_o:\mu = 5`

`H_1:\mu < 5`

To Find : compute the P-value.

Solution:

Sample size = 25

n < 30

So, we will go for t-test

Now we are given that the population standard deviation is 1.2.

`\sqrt{(s)/(n)}=1.2` Where s is the variance

`\sqrt{(s)/(25)}=1.2`

`√(s)=6`

`s = 6^2`

`s = 36`

So, the variance is 36

we require sample standard deviation for t test

So, Sample standard deviation =
`\sqrt{(s)/(n-1)}`

=
`\sqrt{(36)/(25-1)}`

=
`1.2247`

Formula of t-test =
`(m-\mu)/((s)/(√(n)))`

Where s is the standard deviation of sample

Sample mean = 4.73

Mean =
`\mu = 5`

s = 1.2247

n =25

So,
`t=(5-4.73)/((1.2247)/(√(25)))`

`t=1.1023`

So, p value with respect to t-table is 0.1406.

Hence p-value is 0.1406.