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. The population is normally distributed. What is the critical value (given in terms of the value of the test statistic) at a=.01? What is the calculated value of the test statistic? Form the hypotheses according to the question and perform the test at 1% significance level.

Answer & Step-by-step explanation:

Null hypothesis (H0) : μ=100 lbs

Alternative hypothesis (H1) : μ>100 lbs

We must use the t-student distribution because the population standard deviation is unknown.

t-statistic formula:

t = (xbar-m) / (S / (sqrt (n)))

xbar: sample mean

m: hypothesized value

S: sample standard deviation

n: number of observations

t = (104-100) / (10/sqrt (25))

t-statistic = 2

The critical value from the t-student distribution with, 25-1 degrees of freedom and 1% significance level, is 2.4922

Because the t-statistic is less than the critical value, then you do not reject the null hypothesis. Then there is NO statistical evidence to affirm that the average weight population of product X is greater than 100 lbs.