Question

The average speed of greyhound dogs is about 18.4 meters per second. A particular greyhound breeder claims that her dogs are faster than the average greyhound. In a sample of 35 of her dogs, they ran, on the average, 18.7 m/s. Assuming a population standard deviation of 1.5 m/s and a .05 significance level.

Required:
Does this sample data provide evidence that the breeder's claim is correct?

Answer 1

Answer:

The calculated value    Z = 1.183 < 1.96 at 0.05 level of significance

Null hypothesis is accepted

A particular greyhound breeder claims that her dogs are faster than the average greyhound

Step-by-step explanation:

Step(i):-

Given the average speed of greyhound dogs is about 18.4 meters per second.

Size of the sample 'n' = 35

mean of the sample x⁻ = 18.7

Population standard deviation = 1.5m/s

level of significance (∝)  = 0.05

Step(ii):-

Null hypothesis : H₀ : μ = 18.4

Alternative  hypothesis H₁ :  μ ≠ 18.4

Test statistic

              $Z = \frac{x^{-} - mean}{\frac{S.D}{\sqrt{n} } }$

             $Z = \frac{18.7-18.4}{\frac{1.5}{\sqrt{35} } }$

            Z = 1.183

Conclusion:-

The calculated value    Z = 1.183 < 1.96 at 0.05 level of significance

Null hypothesis is accepted

A particular greyhound breeder claims that her dogs are faster than the average greyhound