Question

a) WHO is examining the improvement in life expectancy in an underdeveloped country. Historical data for the population shows a population mean life expectancy of 58.3 years, and with a population standard deviation of 4.52 years. A recent sample of 75 people produced a sample mean of 60.8 years and a sample standard deviation of 2.84 years. Evaluate H0: μ ≤ 58.3 and HA: μ > 58.3 at a .01 level of significance.

b) A medical research team at the Johns Hopkins University is investigating the effectiveness of a new medical treatment for a rare disease. Data indicates that under the current treatment, patients have a mean white blood cell count of 22 cells/cc (cubic centimeter). This distribution is understood to be normally distributed, but the population standard deviation is not known. The new treatment will only be deemed effective if it significantly increases the patient’s white blood cell count above 22 cells/cc.

The team has applied the treatment to a random sample of 10 patients. They have reported the following blood cell counts: 21, 25, 18, 24, 19, 25, 22, 20, 27, 24.

At α = .01, is the new treatment effective?

Answer 1

a)

Let μ be the population mean life expectancy

Hypotheses Statements are

Ho: μ ≤ 58.3

Ha: μ > 58.3

Test statistics (z value as population sigma is given)

p-value

For the test statistic, z = 4.79 and right-tailed test, the p-value is 0

Decision Rule

If the p-value is less than alpha (0.01), we reject the null. Here p-value is less than alpha, So we reject the null

Conclusion

There is statistical evidence to conclude that mean life expectancy is greater than 58.3 years

b)

Need to find mean and SD of the sample

	X	X2
	21	441
	25	625
	18	324
	24	576
	19	361
	25	625
	22	484
	20	400
	27	729
	24	576
Sum =	225	5141

Mean of the sample is given by

Variance is given by

Standard deviation is then

Let μ be the mean white blood cell count

Hypotheses Statements are

Ho: μ ≤ 22

Ha: μ > 22

Test statistics (t value as population sigma is not given)

p-value

For the test statistic, t = 0.535 and right-tailed test, and degree of freedom = 9(10-1), p-value = 0.3027

Decision Rule

If the p-value is less than alpha (0.01), we reject the null.

Here p-value is greater than alpha, So we fail to reject the null

Conclusion

There is statistical evidence to conclude that new treatment is not effective

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