Question

A simple random sample of 40 recorded speeds (in mi/h) is obtained from cars traveling on a specific highway. The sample has a mean of 68.4mi / h and a standard deviation of 5.7mi / h . Use a 0.05 significance level to test the claim that the mean speed of all cars is greater than the posted speed limit of 65mi / h . State the initial and final conclusion.

Answer 1

We need to reject the null hypothesis; there is sufficient evidence to support the claim that the mean speed is greater than 65 miles / hour.

What is normal distribution?

'Normal distribution is a continuous probability distribution wherein values lie in a symmetrical fashion mostly situated around the mean.'

According to the given problem,

Since the sample size is fairly large (n > 30), we use normal distribution.

The null hypothesis tested is

Mean speed of all cars ≤ 65 miles/hour. (µ ≤ 65)

The alternative hypothesis is

Mean speed of all cars > 65 miles/hour. (µ > 65)

Significance level = 0.05

The test statistic used is Z = $\bar{x}$ - µ/σ / √ n, where $\bar{x}$ = 68.4, n = 40, σ = 5.7

Therefore, Z = 68.4 - 65 / 5.7 /√40 = 3.77254177

If the calculated value of test statistic is greater than the critical value at the 0.05 significance level,

Upper critical value = 1.644853627

P-value = P (Z > 3.77254177) = 0.000080796

Hence, we can conclude that we should reject the null hypothesis since there is enough evidence to support the claim that the mean speed is greater than 65 miles / hour.

Learn more about normal distribution here:

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Answer 2

Answer:

Reject the null, there is sufficient