Question

In a sample of 800 people, 420 are in favor of a proposed scoring system. A golf course wants to implement an electronic scoring system where shots are counted by satellites to reduce human error and to show real-time scores at the clubhouse. Is there enough evidence to conclude that the majority of the golfing community is a proponent of the new system at an alpha level of .05. Determine the number of tails for this problem, the critical value and the test statistic.

Answer 1

We accept H₀ with 95 % of Confidence Interval we have enough evidence to conclude that the majority of members agree with the new system

Explanation:

Sample size 800

Sample x₁ = 420 ( number of people in favor of a proposed scoring system), then

p₁ = 420/800 p₁ = 0,525 p₁ = 52,5 % then

q₁ = 1 - p₁ q₁ = 1 - 0,525 q₁ = 0,475

Sample size enought to use the approximation of the binomial didtribution to normal distribution

If significance level is 0,05 α = 0,05

and from z-table we look for z(c) ( z critical value)

z (c) = 1,64

Hypothesis Test:

Null Hypothesis H₀ p₁ = 0,5

Alternative Hypothesis Hₐ p₁ > 0,5

Alternative hypothesis tells us about a one tail-test to the right

To calculate

z(s) = ( p₁ - 0,5) / √ (p₁*q₁) / n

z(s) = 0,025 / √ 0,525*0,475/800

z(s) = 0,025 / √0,000311

z(s) = 0,025/0,01765

z(s) = 1,416

Comparing z(c) and z(s)

z(s) < z(c) 1,416 < 1,64

z(s) is in the acceptance region we accep H₀.