Answer: We will reject the null hypothesis.
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 \\eq 71.5](https://img.qammunity.org/2020/formulas/mathematics/college/7d9t7qnzyqjnu5552g89z6pkwgexsgh9rb.png)
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=(x-\mu)/((\sigma)/(√(n)))\\\\\\x=(80-71.5)/((7.5)/(√(15)))\\\\\\z=4.39](https://img.qammunity.org/2020/formulas/mathematics/college/lhz56jwmga3nduwae1ft9ei8ew2og2oezn.png)
According to test statistic approach:
Since z >1.96
as 4.39>1.96
So, we will reject the null hypothesis.