10.1

1) The Vopstra telecommunication company has increased its branding of phones in the stores that sell them. To varying degrees, the shelves that contain Vopstra phones now have advertizing in the form of small posters.

Different stores contain different amounts of advertizing, and Vopstra would like to know if there is any relationship between amount spent on advertizing(X)and sales of Vopstra phones(Y). A random sample of 50 stores is selected. For each store, the amount in dollars spent on advertizing and the amount in dollars made in sales of Vopstra phones are recorded. The following regression equation is calculated:

^

y= 73.96 + 2.73x

Along with this, the following values were calculated:

SSX = 185.84

SST = 205.50

s_e= 23.60

Vopstra plans on conducting a hypothesis test with 90% confidence and the following hypotheses:

H₀: ₁= 0

H₁: ₁ 0

a)Calculate the test statistic(t)for this test. Give your answer to 4 decimal places.

t =__________

b)The null hypothesisis or is not rejected in this test. ANSWER:_______

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2) A regression model has been developed to analyze the relationship between a response variable Y and an explanatory variable X. A confidence interval is to be constructed for the mean value of Y at a given value of X.

Select whether each change would increase, decrease, or not affect the width of the confidence interval:

-------------------------------------------------------------------------------------------------------------- Increase / Decrease / No effect

a)Increasing the level of confidence --- Increase / Decrease / No effect ---- ANSWER:________

b)Using a larger sample size -- Increase / Decrease / No effect ---- ANSWER:________

c)Choosing a value of X closer tox -- Increase / Decrease / No effect ---- ANSWER:________

d)Having more variation in the values of the response variable about the prediction line Increase / Decrease / No effect ---- ANSWER:________

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Given the data listed in the table, calculate the lower and upper bound for the 95% confidence interval for the mean atX = 9. The regression equation is given byy

^

= b₀+ b₁x.

REGRESSION STATISTICS

stat value

b₀ 9.7

b₁ 0.82

x 7.23

s_e 1.139

SSX 25.89

SST 52.33

n 40

Give your answers to 2 decimal places. You may find thisStudent's t distribution tableuseful.

a)Lower bound =_________

b)Upper bound =_________