Question

Consider the following hypothesis test:

H0: ≤ 26
Ha: > 26

A sample of 40 provided a sample mean of 27.4. The population standard deviation is 6.

Compute the value of the test statistic (to 2 decimals).
What is the p-value (to 4 decimals)?

Answer 1

`z=(27.4-26)/((6)/(√(40)))=1.48`

The p value can be founded with the following probability:

`p_v =P(z>1.476)=0.0694`

Explanation:

Information given

`\bar X=27.4` represent the sample mean

`\sigma=6` represent the population deviation

`n=40` sample size

`\mu_o =26` represent the value to verify

z would represent the statistic

`p_v` represent the p value

System of hypothesis

We want to check if the true mean for this case is higher than 26, the system of hypothesis would be:

Null hypothesis:
`\mu \leq 26`

Alternative hypothesis:
`\mu > 26`

The statistic is given by:

`z=(\bar X-\mu_o)/((\sigma)/(√(n)))` (1)

Replacing the info we got:

`z=(27.4-26)/((6)/(√(40)))=1.48`

The p value can be founded with the following probability:

`p_v =P(z>1.476)=0.0694`