Over me years, it was noticed that the cost of a slice of pizza and the cost of

Question

Over me years, it was noticed that the cost of a slice of pizza and the cost of a subway fare in a certain city seemed to increase by the same amounts Let x represent the cost of a slice of pizza and let y represent the corresponding subway fare. Use the following statistics that were obtained from a random sample of costs (in dollars) of pizza/subway tares to construct a prediction) interval estimate of the subway fare with 99% confidence when the cost of a slice of pizza is $2.80. n = 6 b_0 = 0.03456 b_1 = 0.94502 x = 1.083333 sigma x = 6.50 sigma x^2 = 9.77 s_0 = 0.123 The 99% prediction interval is

Explanation / Answer

Solution:

The regression equation is Y = b0 + b1X

Y = 0.03456 + 0.94502X

When X = $2.80, the estimate subway fare is

Y = 0.03456 + 0.94502 (2.80)

Y = 2.681

99% prediction interval is given by:-

y’ ± t (a/2, n – 2) Se 1 + 1/n + (x0 – x-bar)^2/(x^2 – 1/n (x)^2)

2.681 ± t (0.01/2, 6 - 2) (0.123) 1 + 1/6 + (2.80 - 1.0833)^2/(9.77 - 1/6 (6.5)^2)

2.681 ± 4.604 (0.123) 2.2468

2.681 ± 0.849

2.681 - 0.849, 2.681 + 0.849

1.83, 3.53

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