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

Answer:

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

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

Step-by-step 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.  =  $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$  ~ $t_n_-_1$

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