Please show all work Use the following to answer 4 - 6 Does anyone travel the sp

Question

Please show all work

Use the following to answer 4 - 6 Does anyone travel the speed limit? We wish to see if, on average, traffic is moving faster than the posted speed limit of 65 miles per hour along a certain stretch of Interstate 70. The speeds of an SRS of 12 cars are 70, 65, 70, 71, 64, 72, 76, 72, 83, 68, 70, and 75 miles per hour.

4) Sketch a histogram, stem plot, or dot plot to display the distribution of this data. Should it be safe to use t analysis?

5&6) Assuming that these 12 speeds have a mean of 71.33 and a standard deviation s = 5.07. Test whether, on average, traffic is moving faster, or greater, than 65 miles per hour by testing the hypotheses Ho: m = 65,and Ha: m > 65. What is the value of the t statistic and the corresponding significance value P?

Explanation / Answer

Histogram

Stem plot

MTB > Stem-and-Leaf 'Speed'.

Stem-and-Leaf Display: Speed

Stem-and-leaf of Speed N = 12
Leaf Unit = 1.0

2   6 45
2   6
3   6 8
(4) 7 0001
5   7 22
3   7 5
2   7 6
1   7
1   8
1   8 3

Testing of Hypothesis

Ho: m = 65 Vs Ha : m > 65

One-Sample T

Test of mu = 65 vs not = 65

N   Mean StDev SE Mean      95% CI        T      P
12 71.33   5.07     1.46       (68.11, 74.55) 4.33 0.001

Here P-value is 0.001 and level of significance is 0.05

so P-value < alpha (0.05)

here we reject Ho at alpha = 0.05

that is sample mean is not equal to 65

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