Question

Orville redenbacher states that the average number of calories in a serving of popcorn is 120 with a standard deviation of 15. a nutritionist claims a serving of popcorn is less than 120 calories. he selects 42 different popcorn samples and finds the average calories to be 115 calories per serving. check the nutritionist claim at a=0.01

Answer 1

The hypotheses for the problem are

H0: Average number of calories in a serving of popcorn is 120 calories. That is = 120

H1: Average number of calories in a serving of popcorn is less than 120 calories. That is < 120

Population standard deviation, = 15

Since we know the population standard deviation, we will use one sample z test for the hypothesis test.

Standard error of mean, se = / = 15 / = 2.31455

Test statistic, z = ( - ) / se

= (115 - 120) / 2.31455

= -2.16

For left tail test, p-value = P(z < -2.16) = 0.0154

Since, p-value is greater than 0.01 significance level, we fail to reject null hypothesis H0 and conclude that there is no strong evidence that average number of calories in a serving of popcorn is less than 120 calories.