You are going to study the average speed of vehicles on Highway 61 between Hugo

Question

You are going to study the average speed of vehicles on Highway 61 between Hugo and Forest Lake. Your immediate task is to carry-out a preliminary study to provide information for the design of a more exhaustive scientific investigation. Previous studies have found that the standard deviation of vehicle speeds is 6 [mph]. a. Suppose that observations of 50 randomly selected vehicles yielded a sample mean (arithmetic average) of 65 [mph]. Determine an approximate two-sided 99 percent confidence interval of the mean speed. b. What is the minimum number of randomly selected vehicle speeds that you will need to observe such that the mean speed can be estimated to within plusminus 1 [mph] with 99 percent confidence? c. Suppose two of your classmates, say John and Mary, are assigned the task of collecting vehicle speed data on the highway in question. After each person has separately observed 10 vehicles, what is the probability that John's sample mean will exceed Mary's sample mean by 2 [mph] or more? d. Suppose two of your classmates, say John and Mary, are assigned the task of collecting vehicle speed data on the highway in question. After each person has separately observed 100 vehicles, what is the probability that John's sample mean will exceed Mary's sample mean by 2 [mph] or more?

Explanation / Answer

a)

sig = 6, n = 50, xbar = 65 , c =99%

The formula for two sided confidence interval for mean(mu) is given by,

xbar - E < mu < xbar + E

E = Zc * sig / sqrt(n)

= 2.576 * 6 / 7.0711

= 2.1858

xbar - E = 62.8142

xbar + E = 67.1858

Two sided 99% confidence interval for mean is,

(62.8142 , 67.1858)

b)

Minimum number of randomaly selected vehicle is given by,

n =(1/4)*(Zc / E )2 , E = 1/100 =0.01

= 0.25 *(2.576/0.01)2

= 16589.44

=16589

n = 16589

For solution of part c and d please seperately attach part c and d.

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