Pamela Meyer

2021-12-20

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

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, $n=15$
$\sum x=145.6$
Sample mean, $\stackrel{―}{x}=\sum \frac{x}{n}=\frac{145.6}{15}=9.7067$
Sample standard deviation, $s=1.7689$
Population mean, $\mu =9.6$
Hypothesis test:
The null and alternative hypothesis is
${H}_{0}:\mu =9.6$
${H}_{a}:\mu \ne 9.6$
Test statistics is
$z=\frac{\stackrel{―}{x}-\mu }{\frac{\sigma }{\sqrt{n}}}=\frac{9.7067-9.6}{\frac{1.7689}{\sqrt{15}}}=0.2336$
$\therefore z=0.23$
p-value for two tailed:
p-value $=2p\left(z>0.23\right)$
$=2×0.409046$...(from z-table)
$=0.8181\stackrel{\sim }{=}0.8187$
$\therefore$ p-value $=0.8187$

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