Question

Amy has two ways to travel from her home in Norco to her office in Los Angeles. One is to go via the 10 Freeway, and the other is to go via 60 Freeway. In order to determine which way she should travel on a daily basis, Amy has recorded the travel times for samples of eight trips via the 10 Freeway and eight trips via the 60 Freeway. The following table gives the travel times in minutes) for the sixteen trips: Travel times in minutes 10 Freeway 71, 70, 72, 69, 70, 67, 71, 76 60 Freeway 72, 72, 69, 77, 80, 73, 80, 73 1 Send data to Excel 2 Assume that the two populations of travel times are normally distributed and that the population variances are equal. Can we conclude, at the 0.1 level of significance, that the mean travel times of the two routes are different? Perform a two-tailed test. Then fill in the table below. Carry your intermediate computations to at least three decimal places and round your answers as specified in the table. u O P The null hypothesis: X s The alternative hypothesis: H : The type of test statistic: (Choose one) . 8 O=D OO 020 0#0 O<O OD x ? The value of the test statistic: (Round to at least three decimal places.) The p-value: (Round to at least three decimal places.) Can we conclude that the mean travel times of the two routes are different? Yes No

Please answer neatly and correctly!

Answer 1

The given data is shown in below 10 Freeway 71 70 72 69 70 67 71 76 60 Freeway 72 72 69 77 80 73 8073 Calculate the mean and standard deviation ofthe 10 freeway Σχ Mean ( 71 70 71+76 = 566 8 = 70.75 Σ(-30 . Standard deviation (s,)- n 71-70.75 .+(76-70.75) 8-1 - 2.60 00

Calculate the mean and standard deviation ofthe 60 freeway Σχ Мean (x,) n 80+73 72 72 8 596 = 74.5 Σ(-30). Standard deviation ( s,) n (72-70.50) - +..+(73 70.50) 8-1 = 4.04

Null hypothesis, Ho 4 = 42 Alternative hypothesis, H: 4 4 The type of statistic is: t Calculate the pooled standard deviation (Because, the population variances are equal) (n -1)s; +(n,-1)s nn-2 (8-1)(2.60) +(8-1)(4.04) 8+8-2 = 3.396

The value of the test statistic value is, t 1 Sp. п п, 1 70.75 74.5 1 1 3.396, =-2.208 The degrees of freedom is, df nn-2 =8+8-2 = 16 2 = 14

Calculate the P-value P-value (TDIST(2.208,14,2) (Use MS Excel) = 0.044429 (Round to at least 3 decimal place) = 0.0444 Decision: Reject H, because, the P-value is less than the 0.10 level of significance. 0 Conclusion: the mean travel times of the two routes are different The correct answer is: Yes