A company keeps extensive records on its new salespeople on the premise that sales should increase...

A company keeps extensive records on its new salespeople on the premise that sales should increase with experience. The months on the job x and monthly sales y from a random sample of seven new salespeople resulted in the regression output shown below.

Note that x = 5.8571

Calculate a 95% confidence interval for the mean monthly sales of all employees that have worked at the company for x = 6 months (round to 2 decimal places).

lower bound
upper bound

Expert Solution

ANSWER::

Regression equation :

ŷ = -0.2462 + (1.3152) x

Predicted value of y at x = 6

ŷ = -0.2462 + (1.3152) * 6 = 7.645

Significance level, α = 0.05

Critical value, t_c = T.INV.2T(0.05, 5) = 2.5706

Standard error, se = 1.5770

Standard error of slope, s(b1) = 0.16192

95% Confidence interval :

Lower bound= ŷ - tc*se*√((1/n) + ((x-x̅)²/(se/s(b1)²)))

= 7.645 - 2.5706*1.577*√((1/7) + ((6 - 5.8571)²/(1.577/0.16192)²)) = 6.11

Upper bound = ŷ + tc*se*√((1/n) + ((x-x̅)²/(se/s(b1)²))

= 7.645 + 2.5706*1.577*√((1/7) + ((6 - 5.8571)²/(1.577/0.16192)²)) = 9.18

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orchestra answered 2 years ago

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