Question

A sample of 8 sweet potato slices were fried at 130 degrees using a vacuum fryer. One characteristic of interest to the researchers was internal oil content (measured in millions of grams). It is known that internal oil content is normally distributed. The average oil content of the sample of 8 sweet potato slices was 180 with sample standard deviation 10. The researchers are interested in estimating the average of the internal oil content measurements for sweet potato chips. We want to know whether the average oil content is different than 176 millions of grams. Carry out a hypotheses test with significance level 5%. State the null and alternative hypotheses, test statistics, p-value, and conclusion.

Answer 1

Step 1:

Ho: = 176

Ha: 176

Null hypothesis states that average of the internal oil content measurements for sweet potato chips is 176

Alternatvie hypothesis states that average of the internal oil content measurements for sweet potato chips is not equal to 176

Step 2

Assuming that data is normally distribted and also as the populaion sd is not given, we will use t stat

n = 8

sample mean = 180

sample sd = 10

t = 1.131

p value = TDIST ( 0.05, 7, 2) = 0.2952

Step 3:

t critical for two tailed test = +/- 2.36462425

As tht t stat does not fall in the rejection area, we fail to rejet the Null hypothesis.

Also as the p value (0.2952) is greater than (0.05) we fail to rejet the Null hypothesis.

Hence we do not have sufficient evidence to believe that average of the internal oil content measurements for sweet potato chips is not equal to 176