Question

A researcher collects data on the number of times race horses are raced during their careers. The veterinarian finds that the average number of races a horse enters is 15.3, with a standard deviation of 6.8 in a sample of n = 25 horses.
A 95% confidence for µ, the average number of times a horse races, is given by ___________.

Answer 1

Answer:

95% confidence for µ, the average number of times a horse races

(12.493 , 18.107)

Step-by-step explanation:

Explanation:-

The veterinarian finds that the average number of races a horse enters is 15.3

The mean of the sample x⁻ = 15.3

Given standard deviation of the sample 'S' = 6.8

Given sample size 'n' = 25

Degrees of freedom = n-1 =25-1 =24

The tabulated value 't' = 2.064 at two tailed test 0.95 level of significance

95% confidence for µ, the average number of times a horse races

$(x^{-} - t_{\alpha } \frac{S}{\sqrt{n} } , x^{-} + t_{\alpha }\frac{S}{\sqrt{n} } )$

$(15.3- 2.064 \frac{6.8}{\sqrt{25} } , 15.3 + 2.064\frac{6.8}{\sqrt{25} } )$

(15.3 - 2.80704 ,15.3 +2.80704)

(12.493 , 18.107)

Conclusion:-

95% confidence for µ, the average number of times a horse races

(12.493 , 18.107)