Based on a random sample of 25 units of product X,the average weight is 102 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 alternative hypothesis can be written as H_A: μ 100.(Assume the population is normally distributed. )

Question

Based on a random sample of 25 units of product X,the average weight is 102 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 alternative hypothesis can be written as H_A: μ > 100.(Assume the population is normally distributed. )

Quizplus · Accepted Answer

The null hypothesis can be written as HS1U1B0AS1U1B0: μ ≤ 100. Since the alternative hypothesis is μ > 100, this is a one-tailed test. We can use a t-test since the population standard deviation is not known. The test statistic is:

t = (x̄ - μ) / (s / sqrt(n))

where x̄ is the sample mean, μ is the hypothesized population mean (100), s is the sample standard deviation, and n is the sample size (25).

t = (102 - 100) / (10 / sqrt(25)) = 2

Using a t-table with 24 degrees of freedom (25-1), the critical value at α=0.05 with a one-tailed test is 1.711.

Since our calculated t-value of 2 is greater than the critical t-value of 1.711, we reject the null hypothesis and conclude that there is enough evidence to establish that the average weight for the population of product X is greater than 100 lbs. Therefore, the statement is true.

Based on a Random Sample of 25 Units of Product