Question

The following data is a random sample of annual lightnight deaths from recent years use this data with a 0.01 significance level to test the claim that the mean number of annual lightning deaths is less than the mean of 72.6 deaths from the 1980's. if the mean is now lower than in the past, identify on the serval factors that could explain the decline

Data from 14 recent and consecutive years.

Data: 51, 44, 51, 43, 32, 38, 48, 45, 27, 34, 29, 26, 28, 23

A) Claim, null hypo, Alternantive hypo

B) Solve using the p-value method

C) Solve using the classical method

D) Summary

Answer 1

The data is :

	Data:
	51
	44
	51
	43
	32
	38
	48
	45
	27
	34
	29
	26
	28
	23
Count	14
Average	37.07143
StDev	9.840765

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

Ho: μ = 72.6

Ha: μ < 72.6

This corresponds to a left-tailed test, for which a t-test for one mean, with unknown population standard deviation will be used.

B) and C)

Rejection Region

Based on the information provided, the significance level is α=0.01, and the critical value for a left-tailed test is tc​=−2.65.

The rejection region for this left-tailed test is R=t:t<−2.65

(3) Test Statistics

The t-statistic is computed as follows:

(4) Decision about the null hypothesis

Since it is observed that t=−13.509<tc​=−2.65, it is then concluded that the null hypothesis is rejected.

Using the P-value approach: The p-value is p = 0, and since p=0<0.01, it is concluded that the null hypothesis is rejected.

(D)

Conclusion

It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the population mean μ is less than 72.6, at the 0.01 significance level. Hence the number of night light deaths is less than that was in 1980s. Additionly:

Confidence Interval

The 99% confidence interval is 29.149<μ<44.994.

Graphically

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