An industrial process has one input (X) and one output (Y). The data below, involving 10 measurements of the process, were collected on the output Y corresponding to an input X. Assume that a simple linear regression model is appropriate for this data.

1. A consultant suggested, on the basis of previous experience, that the mean response when X = 4should be less than 27. Conduct a hypothesis test at = 0.05 to determine whether the data supports the consultants assertion. Write down H₀, H_a, the test statistic, decision rule, and your conclusion, based on the above data.[Hint: This test for E(Yh) usesa test statistic that can be calculated withinformation used in the calculation ofthe confidence interval inthe previous part.]

X	3	1	7	5	3	1	6	2	4	6
Y	22	7	43	30	20	15	37	15	23	30