The Next Questions Are Based On The Following Information:
The sales representative for a manufacturer of a new product claims that the product will increase output per machine by at least 29 units per hour.A line manager installs the product on 15 of the machines,and finds that the average increase was only 26 with a standard deviation of 6.2.
-Using a 5% significance level,which of the following statements is true?

Question

Quizplus · Accepted Answer

We need to conduct a one-sample t-test with the following hypotheses:
HS: μ = 29 (The null hypothesis that the product will increase output per machine by at least 29 units per hour)
HA: μ < 29 (The alternative hypothesis that the product will increase output per machine by less than 29 units per hour)

Since the sample size (n) = 15 and the population standard deviation (σ) is not known, we will use the t-distribution.
The test statistic can be calculated as follows:
t = (x̄ - μ) / (s / √n)
Where:
x̄ = 26 (sample mean)
μ = 29 (hypothesized population mean)
s = 6.2 (sample standard deviation)
n = 15 (sample size)

t = (26 - 29) / (6.2 / √15) = -1.693

Using a one-tailed t-test with a 5% level of significance and 14 degrees of freedom (15-1), the critical t-value is -1.761 (found using a t-distribution table or t-distribution calculator).

Since the calculated t-value (-1.693) is greater than the critical t-value (-1.761) and falls in the non-rejection region, we fail to reject the null hypothesis (HS). Therefore, we do not have sufficient evidence to conclude that the new product increases the output per machine by less than 29 units per hour. Hence, we can say that the line manager's result is not statistically significant.

The Next Questions Are Based on the Following Information