What is the life span of a lab mouse? You measured the following life spans (in

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. 819, 998, 701, 901, 805, 970, 384 You may assume for the following questions that the distribution of life span is normal. (a) Calculate the sample mean z, z = 796 8571 (b) Calculate the sample standard deviation s. 208.7578 (c) Calculate the critical value t* for a 83 percent two-sided confidence interval t*- 1.559 (d) Calculate the margin of error m for a two-sided confidence interval. m 123.0098 (e) The lower bound of the two-sided confidence interval is and the upper bound of the two-sided confidence interval is (f) Calculate the critical value t* for the 83 percent lower-bound confidence interval. t (9) Calculate the lower bound of the 83 percent lower-bound confidence interval. We can be 83 percent confident that the mean life span of the lab mouse is more than (h) Calculate the upper bound of the 83 percent upper-bound confidence interval. We can be 83 percent confident that the mean life span of the lab mouse is less than 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 days days

Explanation / Answer

Lower Bound of Confidence Interval = Sample mean - Margin of Error = 796.8571 - 123.0098 = 673.8473

Upper Bound of Confidence Interval = Sample mean + Margin of Error = 796.8571 + 123.0098 = 919.8669

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Critical t-value for 83% lower bound confidence interval and degree of freedom = n-1= 7-1 =6 is 1.0428

This is obtained from interpolation:

at 6 d.o.f : t at 80% is 0.906

t at 85% is 1.134

So, t at 83% is ((1.134 - 0.906) / 5 * 3 ) + 0.906

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t value correspoonding to lower bound 83% is 1.0428

So, 1.0428 = t stats = (x-796.85 / 208.7578 ) * (7^0.5)

x = 879.1301

we can be 83% confident that mean life span of lab mouse is more than 879.1301 days

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t value correspoonding to upper bound 83% is -1.0428

So, -1.0428 = t stats = (x-796.85 / 208.7578 ) * (7^0.5)

x = 714.5699

we can be 83% confident that mean life span of lab mouse is less than 714.5699 days

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