Question

Think about a population mean that you may be interested in and propose a hypothesis test problem for this parameter.

For example, you may believe that the population mean number of times that adults go out for dinner each week is less than 1.5. Your data could be that you spoke with 7 people and found that they went out 1, 0, 1,3, 4, 1, and 1 times last week. You then would choose to test this hypothesis at the .05 (or another) significance level. Assume a random sample.

Answer 1

Here claim is that mean is less than 1.5, so hypothesis is vs

Now for given data sample mean is

Create the following table.

data	data-mean	(data - mean)2
1	-0.5714	0.32649796
0	-1.5714	2.46929796
1	-0.5714	0.32649796
3	1.4286	2.04089796
4	2.4286	5.89809796
1	-0.5714	0.32649796
1	-0.5714	0.32649796

So

Test statistics is

P value is TDIST(0.14,6,1)=0.447

As P value is greater than alpha=0.05, we fail to reject the null hypothesis

Hence we do not have sufficient evidence to support the claim that mean is less than 1.5