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)

alpha = 0.01 , as the level of signifcance is 1 %

H0 : The average life span is 16.5 years , mu != 16.5 years

Ha : The avergae life span is less than 16.5 years , mu < 16.5 years

test : t test

b)

we shall use t test , as the sample size is less than 30 . If the sample size is more than 30 then we shall use a z test

c)

we knwo that the confidence interval is given as

mean +- t*sd/sqrt(n) , also The appropriate t-multiplier for a 99% confidence interval for the mean ist0.005,14 = 2.98. please keep the t table handy

10.6 +- 2.98*3.25/sqrt(20) , this means the range is

8.43 and 12.76

d)

Interpretation:

This can be interpreted as that the true mean of the population would lie in the range 8.43 to 12.76 and we are 99% confident in making this statement

Please note that we can answer only 4 subparts of a question at a time , as per the answering guidelines

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