Question

California Speeding: Listed below are the recorded speeds (in mi/hr) of randomly selected cars traveling on a section of Highway 405 in Los Angeles. That part of the highway has a posted speed limit of 65 mi/hr. Assume the standard deviation of speeds is 5.7 mi/hr. Use a 1% significance level to test the claim that sample is from a population with a mean weight that is greater than 65 mi/hr. 68 68 72 73 65 74 73 72 68 65 65 73 66 71 68 74 66 71 65 73 59 75 70 56 66 75 68 75 62 72 60 73 61 75 58 74 60 73 58 75

Answer 1

The data is :

	Data
	68
	68
	72
	73
	65
	74
	73
	72
	68
	65
	65
	73
	66
	71
	68
	74
	66
	71
	65
	73
	59
	75
	70
	56
	66
	75
	68
	75
	62
	72
	60
	73
	61
	75
	58
	74
	60
	73
	58
	75
Count	40
Mean	68.375
SD	5.669022889

The provided sample mean is and the known population standard deviation is , and the sample size is

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

Ho:

Ha:

This corresponds to a right-tailed test, for which a z-test for one mean, with known population standard deviation, will be used.

(2) Rejection Region

Based on the information provided, the significance level is α=0.01, and the critical value for a right-tailed test is zc​=2.33.

The rejection region for this right-tailed test is R={z:z>2.33}

(3) Test Statistics

The z-statistic is computed as follows:

(4) The decision about the null hypothesis

Since it is observed that z=3.745>zc​=2.33, it is then concluded that the null hypothesis is rejected.

Using the P-value approach: The p-value is p=0.0001, and since p=0.0001<0.01, it is concluded that the null hypothesis is rejected.

(5) Conclusion

It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the population mean μ is greater than 65, at the 0.01 significance level.

Graphically

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