# The average life span of a Golden Retriever is said to be 9.

The average life span of a Golden Retriever is said to be 9.6 years. In a random sample of 15 Golden Retrievers, the following life spans were found:
6.8 10.2 9.5 13 9.9 7.0 8.3 8.9 11.2 10 9.8 13 9.8 9.5 8.7
At a 5% significance level, if we do a complete hypothesis test to test eh claim that the average life span of Golden Retrievers is 9.5, the p-value and conclusion are:
p-value = 0.8187, fail to reject the null hypothesis
p-value = 0.8153, fail to reject the null hypothesis
p-value = 0.8187, reject the null hypothesis
p-value = 0.8153, reject the null hypothesis

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aquariump9
Given:
The average lifespan of a golden retriever is a set to be 9.6 years in the random sample of 15 golden retriever the following life span were found.
From tbe given data
Sample size, $$\displaystyle{n}={15}$$
$$\displaystyle\sum{x}={145.6}$$
Sample mean, $$\displaystyle\overline{{{x}}}=\sum\frac{{x}}{{n}}=\frac{{145.6}}{{15}}={9.7067}$$
Sample standard deviation, $$\displaystyle{s}={1.7689}$$
Population mean, $$\displaystyle\mu={9.6}$$
Hypothesis test:
The null and alternative hypothesis is
$$\displaystyle{H}_{{0}}:\mu={9.6}$$
$$\displaystyle{H}_{{a}}:\mu\ne{9.6}$$
Test statistics is
$$\displaystyle{z}={\frac{{\overline{{{x}}}-\mu}}{{\frac{\sigma}{\sqrt{{n}}}}}}={\frac{{{9.7067}-{9.6}}}{{\frac{{1.7689}}{\sqrt{{{15}}}}}}}={0.2336}$$
$$\displaystyle\therefore{z}={0.23}$$
p-value for two tailed:
p-value $$\displaystyle={2}{p}{\left({z}{>}{0.23}\right)}$$
$$\displaystyle={2}\times{0.409046}$$...(from z-table)
$$\displaystyle={0.8181}\stackrel{\sim}{=}{0.8187}$$
$$\displaystyle\therefore$$ p-value $$\displaystyle={0.8187}$$
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godsrvnt0706
Since p-value is greater than significance level 0.05, we fail to reject null hypothesis.
p-value = 0.8187, fail to reject the null hypothesis.
Therefore the correct option is A
RizerMix