Question

How many tissues should a package of tissues​ contain? Researchers have determined that a person uses an average of 60 tissues during a cold. Suppose a random sample of 10 comma 000 people yielded the following data on the number of tissues used during a​ cold: x overbar equals 53 comma s equals 23. We want to test the alternative hypothesis Upper H Subscript a​: muless than60. State the correct rejection region for alpha equals 0.05 .

Answer 1

Null hypothesis:
`\mu \geq 60`

Alternative hypothesis:
`\mu <60`

Since the sample size is large enough we can assume that the distribution for the statistic is normal so then in order to find the critical value for this test taking in count the significance level given of 0.05 we need to look in the normal standard distribution a value who accumulates 0.05 of the area in the left and would be:

`z_(crit)= -1.64`

Explanation:

For this case we have the following data given:

`\bar X = 53` represent the sample mean

`s = 23` represent the sample deviation

`n = 10000` represent the sample size.

We want to test for this case if the true mean is less than 60 so then the system of hypothesis are:

Null hypothesis:
`\mu \geq 60`

Alternative hypothesis:
`\mu <60`

Since the sample size is large enough we can assume that the distribution for the statistic is normal so then in order to find the critical value for this test taking in count the significance level given of 0.05 we need to look in the normal standard distribution a value who accumulates 0.05 of the area in the left and would be:

`z_(crit)= -1.64`