Question

4 randomly selected cans of pumpkin pie mix contain a mean of 30 ounces / per can . Verify the claim that an average of pie mix in one can exceeds 31.5 ounces if the contents of the cans are normally distributed with a standard deviation 2 ounces.

List the conditions for testing a population mean, and indicate whether all conditions for test are satisfied here.

Answer 1

Here, we use the one sample t test to test whether the difference between the sample mean and the population mean.

Here, = 30 , s = 2

The population mean, = 31.5

To test,

H₀ : The average pie mix is greater than 31.5

H₁ : The average pie mix is not greater than 31.5

Here, we take level of significance = 0.05

DF = n-1 = 4-1 = 3

The test statistic is, t = ( - )/( s/n )

= -1.5

At level 0.05, and df = 3, critical value of t = 2.353

As the critical value of t is greater than the test statistic, we reject the null hypothesis at alpha= 0.05.

Hence, the average pie mix does not exceed 31.5.