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In: Statistics and Probability

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

A company keeps extensive records on its new salespeople on the premise that sales should be linearly related to experience. A random sample of four new salespeople produced the data on experience and sales shown in the table.

Months on Job	Monthly Sales ($1000)
2	3
5	4
3	4
8	6

Preliminary calculations are given below.

	x	y	x²	y²	xy
	2	3	4	9	6
	5	4	25	16	20
	3	4	9	16	12
	8	6	64	36	48
Total	18	17	102	77	86

Part A: Find the least square line predicting monthly sales by months on job.

	a. y with hat on top = 0.457+0.843x
	b. y with hat on top = 2.216+0.453x
	c. y with hat on top = 3.692+0.124x
	d. y with hat on top = -9.570+64.5x

Part B: Find s, the estimated standard deviation of random error

	a. 0.228
	b. 0.477

	c. 0.456
	d. 4.750

Part C: Test if monthly sales is linearly related to months on job at 0.05 level of significance. State hypotheses.

	a. H0: beta0 = 0; Ha: beta0 not = 0
	b. H0: beta1 = 0; Ha: beta1 > 0

	c. H0: beta0 = 0; Ha: beta0 > 0
	d. H0: beta1 = 0; Ha: beta1 not = 0

Part D: Test if monthly sales is linearly related to months on job at 0.05 level of significance. Find the value of test statistic.

	a. 0.452
	b. 0.477

	c. 4.342
	d. 4.750

Part E: Test if monthly sales is linearly related to months on job at 0.05 level of significance. Find the rejection region.

	a. t<-3.182 and t>3.182
	b. t>2.920

	c. t<-4.303 and t>4.303
	d. t>2.353

Part F: Test if monthly sales is linearly related to months on job at 0.05 level of significance. What is your conclusion at 0.05 level of significance?

	a. Reject H0. Sufficient evidence that monthly sales is not linearly related to months on job.
	b. Do not reject H0. Insufficient evidence that monthly sales is linearly related to months on job.

	c. Do not reject H0. Insufficient evidence that monthly sales is not linearly related to months on job.
	d. Reject H0. Sufficient evidence that monthly sales is linearly related to months on job.

Part G: Find a 95% confidence interval of the slope.

	a. (0.207, 0.697)
	b. (0.004, 0.900)

	c. (0.148, 0.756)
	d. (0.121, 0.783)

Part H: Interpret the confidence interval of the slope. With 95% confidence, …

	a. Experience on job is expected to increase by at least the lower limit and at most the upper limit for each $1000 increase in monthly sales, valid for $3000 to $6000 monthly sales.
	b. Monthly sales are expected to increase by at least the lower limit and at most the upper limit for each additional month experience on job, valid for 2-8 months experience on job.

	c. Monthly sales are expected to decrease by at least the lower limit and at most the upper limit for each additional month experience on job, valid for 2-8 months experience on job.
	d. Experience on job is expected to decrease by at least the lower limit and at most the upper limit for each $1000 increase in monthly sales, valid for $3000 to $6000 monthly sales.

Part I: Find the value of coefficient of correlation.

	a. 0.951
	b. -0.049

	c. -0.951
	d. 0.049

Part J: What kind of correlation does the coefficient imply?

	a. A strong positive correlation between monthly sales and experience on job.
	b. A weak positive correlation between monthly sales and experience on job.

	c. A weak negative correlation between monthly sales and experience on job.
	d. A strong negative correlation between monthly sales and experience on job.

Part K: Find the value of coefficient of determination.

	a. 0.998
	b. 0.002

	c. 0.096
	d. 0.904

Part L: Interpret the coefficient of determination.

	a. It’s the proportion of sample variation in months on job that cannot be explained by using months on job to predicting monthly sales in a linear model.
	b. It’s the proportion of sample variation in monthly sales that can be explained by using months on job to predicting monthly sales in a linear model.

	c. It’s the proportion of sample variation in months on job that can be explained by using months on job to predicting monthly sales in a linear model.
	d. It’s the proportion of sample variation in monthly sales that cannot be explained by using months on job to predicting monthly sales in a linear model.

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Expert Solution

orchestra answered 1 year ago

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