Question

How many tissues should the Kimberly Clark Corporation package of Kleenex® contain? Researchers determined that 60 tissues is the mean number of tissues used during a cold. Suppose a random sample of 100 Kleenex users yielded the following data on the number of tissues used during a cold: sample mean = 52, sample std deviation = 22.Give the null and alternative hypotheses to determine if the number of tissues used during a cold is less than 60.

Answer 1

Null Hypothesis,
`H_0` :
`\mu \geq` 60 tissues

Alternate Hypothesis,
`H_A` :
`\mu` < 60 tissues

Explanation:

We are given that 60 tissues is the mean number of tissues used during a cold.

Suppose a random sample of 100 Kleenex users yielded the following data on the number of tissues used during a cold: sample mean = 52, sample std deviation = 22.

Let
`\mu` = mean number of tissues used during a cold.

So, Null Hypothesis,
`H_0` :
`\mu \geq` 60 tissues

Alternate Hypothesis,
`H_A` :
`\mu` < 60 tissues

Here, null hypothesis states that the mean number of tissues used during a cold is more than or equal to 60.

On the other hand, alternate hypothesis states that the mean number of tissues used during a cold is less than 60.

The test statistics that would be used here is One-sample t test statistics as we don't know about population standard deviation i.e;

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

Hence, the above hypothesis is appropriate for the given situation.