Question

What is the difference in average daily hotel room rates between Minneapolis and New Orleans? Suppose we want to estimate this difference by taking hotel rate samples from each city and using a 98% confidence level. The data for such a study follow. Use these data to produce a point estimate for the mean difference in the hotel rates for the two cities. Assume the population variances are approximately equal and hotel rates in any given city are normally distributed.

Minneapolis		New Orleans
nM=20		nNO=22
x¯M=$128		x¯NO=$144
sM=$24		sNO=$29

Choose the correct answer.

a) −$42.60≤μ1−μ2≤−$7.40       Point Estimate = −$15

    b)  −$36.02≤μ1−μ2≤     $4.02       Point Estimate = −$16

c) −$32.80≤μ1−μ2≤−$7.20       Point Estimate = −$10

d)−$35.40≤μ1−μ2≤−$4.60       Point Estimate = −$16

e) −$40.40≤μ1−μ2≤−$9.60       Point Estimate = −$15

Answer 1

ans-> b) Point estimate = 128 - 144 = -16

Here, 21 = 128.00, 81 = 24.00, n1 = 20,02 = 144.00, S2 = 29.00, n2 = 22 and pooled variance 2. _ (n1 – 1)sí + (n2 – 1)s to - = 715.125000 nu + n2 – 2 The margin of error is 1 1 M E = t 1-0.98 m+n2-2 * $p * V V nin2 1 — + 8, nitna-2 * Sp *1 = too10,40 * 26.7418+ Vamo tudi = 2.423257 + 26.7418 * 20 + - = 20.021136 a 98 percent confidence interval for the differnce in population means (ui – u2 ) is 1 = #1 – 22 Espv + * t 1-0.980 40 V nin2 2 = 21 - 22 EME = (128.000 – 144.000) – 20.021136 = -16.000 – 20.021136 = (-36.021136, 4.021136) ^(-36.02, 4.02)