Question

The sponsors of televisions shows targeted at the market of 5- to 8-year olds want to test the hypothesis that children watch television AT MOST 20 hours per week. The population of viewing hours per week is known to be normally distributed with a standard deviation of 6 hours. A market research firm conducted a random sample of 30 children in this age group. The resulting data follow:

19.5	29.7	17.5	10.4	19.4	18.4
14.6	10.1	12.5	18.2	19.1	30.9
22.2	19.8	11.8	19.0	27.7	25.3
27.4	26.5	16.1	21.7	20.6	32.9
27.0	15.6	17.1	19.2	20.1	17.7

At a .10 level of significance, use Excel to test the sponsors' hypothesis.

Do not eject Null Hypothesis. There is not strong evidence that children watch more than 20 hours per week.

Reject Null. The evidence suggests children watch more than 20 hours per week

Reject Null. The evidence suggests children watch about 20 hours per week

Do not reject Null hypothesis. The evidence suggests children watch more than 20 hours per week.

Answer 1

Here we want to test the hypothesis that children watch television AT MOST 20 hours per week.

So the null hypothesis and the alternative hypothesis for one sample z test ( because population standard deviation is known) is as follows:

Let's use minitab:

First enter the data in minitab column:

The command is Stat>>>Basic Statistics >>1 sample Z...

Fill the required information

Look the following image:

Then click on OK, so we get the following output

From the above output, we get

Z test statistic value = 0.24

p-value = 0.596

Since p-value > 0.10 so we fail to reject the null hypothesis.

So at 10% level of significance there is not sufficient evidence to conclude that children watch television AT MOST 20 hours per week.