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

Question

Over the 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 fares to construct a prediction interval estimate of the subway fare with 99% confidence when the cost of a slice of pizza is $1.80. n = 6 b_0 = 0.03456 b_1 = 0.94502 x^bar = 1.0833333 sigma_x = 6.50 sigma x^2 = 9.77 s_c = 0.123 The 99% prediction interval is

Explanation / Answer

tcrit = +/- 4.6041 for degree of freedom, df = n-2 = 6-2 = 4, se = 0.123

y_hat = 0.03456 + 0.94502*1.80 = 1.735596

lower bound = y_hat - tcrit*se = 1.735596 - 4.6041*0.123 = 1.17
lower bound = y_hat - tcrit*se = 1.735596 + 4.6041*0.123 = 2.30

1.17 < y < 2.30

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