Question

Page 2 of 2 A manufacturer of widgets wants to test a new widget-producing machine to determine if it can make an average of 20 widgets per second before deciding to invest in the machine. The standard to reject the new machine is if it makes an average of less than 20 widgets per second. Here are data from a small random sample: 15.6 16.2 22.5 20.5 16.4 19.4 19.6 17.9 12.7 14.9 Assuming the population follows a normal distribution, is there evidence that the new machine should be rejected at the 0.01 significance level? State the hypotheses, check the conditions, calculate the test statistic, find the p-value, and make a conclusion in a complete sentence related to the scenario.

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis: μ = 20
Alternative Hypothesis: μ < 20

Rejection Region
This is left tailed test, for α = 0.01 and df = 9
Critical value of t is -2.821.
Hence reject H0 if t < -2.821

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (17.57 - 20)/(2.9522/sqrt(10))
t = -2.603

P-value Approach
P-value = 0.0143
As P-value >= 0.01, fail to reject null hypothesis.

there is significant evidence to conclude that the the mean the is less than 20 widgets per second