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 advrertizmgr 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: g}: 77.54 + 3.28x Along with this, the following values were calculated: SSX = 154.70 SST = 200.25 59 = 21.38 Vopstra plans on conducting a hypothesis test with 95% confidence and the following hypotheses: H0: [31 = 0 H1: [31 2 0 You may nd this Student's t distribution table useful. 3) Calculate the test statistic (t) for this test. Give your answer to 4 decimal places. b) The null hypothesis rejected in this test. A regression model has been developed to analyze the relationship between a response variable Y and an explanatory variable X. A prediction interval is to be constructed for an individual value on for a given value of X. Select wheth er each change would increase, decrease, or not affect the Width of the prediction interval. Increase Decrease Not affect a) Decreasing the level of confidence 0 O O b) Using a larger sample size c) Choosing a value of X further away from Q 000 000 000 d) Having less variation in the values of the response variable about the prediction line (given the data listed in the table, calculate the lower and upper bound for the 90% confidence interval for the mean at X : 9. The regression equation is given by y : b0 + blx. Regression Statistics Statistic Value bD 6.0 b1 1.01 7.00 se 1.605 SSX 29.11 SST 47.93 n 40 Give your answers to 2 decimal places. You may find this Student's t distribution table useful. a) Lower bound = \\:| b) Upper bound = E