Answer:
a) Null hypothesis: H₀ : μ = 57
Alternative hypothesis H₁ : μ ≠ 57
b) The calculated value t =4.077 > 1.6896 at 99% of confidence degrees of freedom.
Natalie is trying to prove the new technique is an improvement over the old technique.
Step-by-step explanation:
<u>Step:-(i)</u>
The average speed of a volleyball serve is 57 miles per hour.
μ = 57 miles per hour
Average speed using the new technique was 58.9 miles per hour, with a standard deviation of 2.8 miles per hour.
sample mean x⁻ = 58.9 miles per hour
Standard deviation S = 2.8 miles per hour.
<u>Step:-(ii)</u>
Null hypothesis: H₀ : μ = 57
Alternative hypothesis H₁ : μ ≠ 57
Degrees of freedom γ=n-1
The test statistic
t = 4.077
Degrees of freedom γ=n-1 = 35-1 =34
tₐ = 2.0322
<u>The calculated value t =4.077 > 1.6896 at 99% of confidence degrees of freedom.</u>
<u>The Natalie is not trying to prove the new technique is an improvement over the old technique.</u>