Question

What is the life span of a lab mouse? You measured the following life spans (in days) for a certain standard inbred laboratory strain.

1062, 1285, 412, 828, 602, 602, 763, 854, 666, 489

You may assume for the following questions that the distribution of life span is normal.

(a) Calculate the sample mean x¯.x¯. x¯=x¯= Answer

(b) Calculate the sample standard deviation s.s. s=s= Answer

(c) Calculate the critical value t⋆t⋆ for a 92 percent two-sided confidence interval. t⋆=t⋆= Answer

(d) Calculate the margin of error mm for a two-sided confidence interval.  m=m= Answer

(e) The lower bound of the two-sided confidence interval is Answer and the upper bound of the two-sided confidence interval is Answer .

(f) Calculate the critical value t⋆t⋆ for the 92 percent lower-bound confidence interval. t⋆=t⋆= Answer

(g) Calculate the lower bound of the 92 percent lower-bound confidence interval. We can be 92 percent confident that the mean life span of the lab mouse is more than Answer days.

(h) Calculate the upper bound of the 92 percent upper-bound confidence interval. We can be 92 percent confident that the mean life span of the lab mouse is less than Answer days.

Please note that you must decide which of the three confidence intervals you wish to calculate before you look at the data. In particular, the confidence intervals in (g) and (h) are not simultaneously valid.

Answer 1

a) The sample size is n=10. The provided sample data along with the data required to compute the sample mean and sample variance are shown in the table below:

	LifeSpan	LifeSpan2
	1062	1127844
	1285	1651225
	412	169744
	828	685584
	602	362404
	602	362404
	763	582169
	854	729316
	666	443556
	489	239121
Sum =	7563	6353367

The sample mean is computed as follows:

(b)Also, the sample variance is

Therefore, the sample standard deviation s is

(c)The critical value for α=0.08 and df = n-1 = 9 degrees of freedom is

(d) The margin of error is given by:

(e) We need to construct the 92% confidence interval for the population mean μ. The following information is provided:-

Sample Mean =	756.3
Sample Standard Deviation (s) =	265.303
Sample Size (n) =	10

The corresponding confidence interval is computed as shown below:-

Therefore, based on the data provided, the 92% confidence interval for the population mean is 590.802<μ<921.798, which indicates that we are 92% confident that the true population mean μ is contained by the interval (590.802, 921.798)

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