7. The Colorado-based Morris Animal Foundation conducted a Last month, that incl

Question

7. The Colorado-based Morris Animal Foundation conducted a Last month, that included 3,000 purebread Golden retreivers. study. the study recording the average life span of followinig sample Golden Retreivers (to the nearest year) 35 points) 4 5 6 7 8 9 10 11 11 11 11 11 11 12 12 13 14 14 15 16 The sample yielded an average of 10.6 years, with a deviation of 3.25 year. Long term trends, where data was last colected in 1976 shows that golden average of 16.5 years with a standard deviation of 4.1 years, back then. Using the information provided. answer the following question: Does this mean that the average life span is now less than 16.5 years? Use a 1% level of significance to answer this question. (a) What is the level of significance? State the null and alternate hypotheses algebraically/not verablly. Will you use a left-tailed, right-tailed. or two-tailed test? Ho- use: the standard normal or the Student's t (b) Identify the sampling distribution you w Explain the rationale for your choice. (e) Construct a 99% confidence interval for the mean age of Golden Retreivers. (d) Interpret the confidence interval you just constructed. golden retrewers (e) How many more three-eieks should be sample to be certain that our confidence interval captures the population mean, with a margin of error of 0.01? (0 Find the z-value and the p-value corresponding to the sample mean.

Explanation / Answer

(a) = 0.01, Ho: 16.5, Ha: < 16.5, Test: Right-tail t- test

(b) We use the t- distribution since we are given the sample standard deviation

(c) n = 20   

x-bar = 10.6     

s = 3.25     

% = 99     

Standard Error, SE = s/Ön =    3.25/20 = 0.726722093

Degrees of freedom = n - 1 =   20 -1 = 19   

t- score = 2.860934604     

Width of the confidence interval = t * SE =     2.86093460403877 * 0.726722092687432 = 2.079104382

Lower Limit of the confidence interval = x-bar - width =      10.6 - 2.07910438248894 = 8.520895618

Upper Limit of the confidence interval = x-bar + width =      10.6 + 2.07910438248894 = 12.67910438

The 99% confidence interval is [8.52, 12.68]

(d) We are 95% confident that the true mean life lies within the above interval

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