Question

Out of the last 48 NBA Championships, 15 of the final games had a winning team score greater than 110 points. Use a 0.01 significance level to test the claim that the true population percentage of NBA Championship final games with a winning score greater than 110 points is more than 30%.

• Label each statement. The one with EQUALITY gets the H₀:

• H₀ (null hypothesis):
• H₁ (alternative hypothesis):

• Write down the value given for the significance level:

• Write the Critical value (the Table value) here:

• Now use your calculator or the formula to tell me the calculated value (known as the “test statistic”):

• What is the P-value:

• REJECT H₀:   YES or NO

• What is your conclusion?

If the winning score of the final game of the 2019 championships is greater than 110 points, do you think that will be an unusual result?

Answer 1

Sample size (n) = 48

Number of NBA Championship final games with a winning score greater than 110 points (x) = 15

= x/n = 15/48 = 0.3125

The hypotheses are

H₀: p = 0.30

H_a: p > 0.30

The given significance level (α) = 0.01

One sided z critical values at α = 0.01 is Z_α = Z_c = 2.33

The critical value is 2.33

Test statistics: Z = ( – P₀) / √ (P₀ (1 - P₀) / n)

                           Z = (0.3125 – 0.30) / √ ((0.30)*(1-0.30)/48)

                           Z = 0.189

Decision rule: Reject H₀ if Z > Z_c.

Using critical value approach, Z = 0.189 < Z_c = 2.33. Since test statistics is not lies in rejection region so we failed to reject null hypothesis.

This is one sided test so we find the right tailed probability.

P value = P(Z > 0.189) = (1 - NORM.S.DIST(0.189,TRUE)).. (Using excel function)

The P value is 0.425

Using p value approach, P value = 0.425 > α = 0.01 so we failed to reject H₀.

Conclusion: We failed to reject H₀. There is no enough evidence to support the claim that the true population percentage of NBA Championship final games with a winning score greater than 110 points is more than 30% at the 0.01 level of significance.

If the winning score of the final game of the 2019 championships is greater than 110 points.

This result is usual because event with a probability i.e. p-value is not less than 0.01.