Question

The average weight of a male labrador retriever is believed to be well-approximated by a normal distribution with mean 71.5 lbs and standard deviation 7.5 lbs. A veterinarian is skeptical of this claim and takes a random sample of 15 labs that come into her clinic. The 15 labs have an average weight of 80 lbs. Use the test statistic approach at the 5% level to test if the vet’s data suggests that our original belief is incorrect.

Answer 1

Answer: We will reject the null hypothesis.

Step-by-step explanation:

Since we have given that

Mean μ = 71.5 lbs

Standard deviation σ = 7.5 lbs

So, the hypothesis are given below:

$H_0:\mu =71.5\\\\H_1:\mu \neq 71.5$

Since α = 5% level of significance = 0.05

So, there is two tail test.

Critical values of z are 1.96 and -1.96.

So, we will reject H₀ if z<-1.96 or z>1.96

So, first we will find the value of z.

$z=\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}\\\\\\x=\dfrac{80-71.5}{\dfrac{7.5}{\sqrt{15}}}\\\\\\z=4.39$

According to test statistic approach:

Since z >1.96

as 4.39>1.96

So, we will reject the null hypothesis.