Question

In a research report, Richard H. Weindruch of the UCLA Medical School claims that mice with an average life span of 32 months will live to be about 40 months old when 40% of the calories in their diet are replaced by vitamins and protein. Is there any reason to believe that μ < 40 if 64 mice that are placed on this diet have an average life of 38 months with a standard deviation of 5.8 months? Use a P-value in your conclusion.

Answer 1

The average life of the mice that are placed on this diet is less than 40 months.

Explanation:

Consider the provided information.

When 40% of the calories in their diet are replaced by vitamins and protein. Is there any reason to believe that μ < 40.

The null and alternative hypothesis are:

`H_0:\mu=40\\H_a:\mu<40`

64 mice that are placed on this diet have an average life is 38 months with a standard deviation of 5.8 months.

Therefore,
`n = 64, \bar x=38\ and\ \sigma=5.8`

Use the formula:
`z=(\bar x-\mu)/((\sigma)/(√(n) ))`

Substitute the respective values in the above formula.

`z=(38-40)/((5.8)/(√(64) ))`

`z=-(2)/((5.8)/(8))\approx-2.76`

Now using the table
`P(Z<z)=0.029`

The p value is smaller than 0.05 so reject the null hypothesis.

Therefore, the average life of the mice that are placed on this diet is less than 40 months.