Question

A consumer group tested 11 brands of vanilla yogurt and found the numbers below for calories per serving.

125 160 150 115 125 110 165 160 115 125 90

​a) Check the assumptions and conditions.

​b) A diet guide claims that you will get an average of 120 calories from a serving of vanilla yogurt. Use an appropriate hypothesis test to comment on their claim.

Answer 1

a)

Each brand is independent from other.

It is given that sample is random sample.

Following is the box plot:

Box plot shows that there is no outlier and disribution is approximately symmetric so normality condition has been fulfilled.

b)

Following is the output of descritpive statistics:

Descriptive statistics
	X
count	11
mean	130.91
sample standard deviation	24.37
sample variance	594.09
minimum	90
maximum	165
range	75

That is we have

Hypotheses are:

So test statitics will be

Degree of freedom: df=n-1=10

The p-value using excel function "=TDIST(1.483,10,2)" is: 0.1689

Since p-value is greater than 0.05 so we fail to reject the null hypothesis.