Question

Based on a random sample of 25 units of product X, the average weight is 104 lbs., and the sample standard deviation is 10 lbs. We would like to decide if there is enough evidence to establish that the average weight for the population of product X is greater than 100 lbs. Assume the population is normally distributed. At alpha = .01. What is the calculated value of the test statistic? Construct the hypotheses according to the question and perform the test at 1% significance level.

Answer 1

Solution :

Given that,

Population mean = = 100

Sample mean = = 104

Sample standard deviation = s = 10

Sample size = n = 25

Level of significance = = 0.01

This is a right tailed test.

The null and alternative hypothesis is,

Ho: 100

Ha: 100

The test statistics,

t = ( - )/ (s/)

= ( 100 104 ) / ( 10 / 25)

= 2

p-value = 0.0285

The p-value is p = 0.0285 > 0.01. it is concluded that the null hypothesis is fail to reject.

Conclusion:

It is concluded that the null hypothesis Ho is fail to reject. Therefore, there is not enough evidence to claim that the average

weight for the population of product X is greater than 100 lbs., at the 0.01 significance level.