Question

instructions: For any hypothesis test, be sure to state your Ho and Ha, test statistic, p-value, and conclusion the words of the problem. For any confidence interval be sure to interpret the interval in the words of the problem. Round answers to the thousandths place.

2b)

A study is done to determine if Company A retains its workers longer than Company B. Company A samples 20 workers, and their average time with the company is five years with a standard deviation of 1.2 years. Company B samples 20 workers, and their average time with the company is 4.5 years with a standard deviation of 0.8. The populations are normally distributed. Is there evidence at the 5% significance level that the true mean retention time is different for A than for B? You may use a confidence interval or a hypothesis test.

2C)

Consider a small scale example, comparing how temperatures have changed in the US from1968 to 2008. The daily high temperature reading on January 1 was collected in 1968 and 2008 for 51 randomly selected locations in the continental US. The locations are the same for both years. Then the difference between the two readings (temperature in 2008 - temperature in 1968) was calculated for each of the 51 different locations. The average of these 51 values was 1.1 degrees with a standard deviation of 4.9 degrees. Does the data provide evidence that the true mean temperature is different in 2008 than in 1968? Justify fully at the 5% significance level.

Answer 1

2b) The hypothesis being tested is:

H0: µ1 = µ2

H1: µ1 ≠ µ2

Company A	Company B
5	4.5	mean
1.2	0.8	std. dev.
20	20	n
	38	df
	0.5000	difference (Company A - Company B)
	1.0400	pooled variance
	1.0198	pooled std. dev.
	0.3225	standard error of difference
	0	hypothesized difference
	1.550	t
	.1293	p-value (two-tailed)

The p-value is 0.1293.

Since the p-value (0.1293) is greater than the significance level (0.05), we fail to reject the null hypothesis.

Therefore, we cannot conclude that the true mean retention time is different for A than for B.

2C) The hypothesis being tested is:

H0: µd = 0

Ha: µd ≠ 0

The test statistic, t = xd/sd/√n = 1.1/4.9/√51 = 1.60

The p-value is 0.1152.

Since the p-value (0.1152) is greater than the significance level (0.05), we fail to reject the null hypothesis.

Therefore, we cannot conclude that the true mean temperature is different in 2008 than in 1968.

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