Question

1) Use either the critical value or p-value method for testing hypotheses.
2) Identify the null and alternative hypotheses, test statistic, P-value (or range of P-values), and critical value(s).
3) State your final conclusion that addresses the original claim. Include a confidence interval as well and restate this in your original conclusion.

Any basketball fan know that Shaquille O’Neal, one of the NBA’s most dominant centers of the last twenty years, always had difficulty shooting free throws. Over the course of his career, his overall made free-throw percentage was 53.3%. During one off season, Shaq had been working with an assistant coach on his free-throw technique. During the next season, a simple random sample showed that Shaq made 26 of 39 free-throw attempts.

Test the claim at the 0.05 Significance Level that Shaq has significantly improved his free-throw shooting.

Answer 1

p= 53.3%= 0.533, n=39, x=26, =5%=0.05

Ho: P = 0.533

Ha: P > 0.533

Calculate tests statistics

test statistics = 1.68

P-Vlaue = 1 - P(Z < 1.68)

using z table we get

P(Z < 1.68) = 0.9535

P-Value = 1 - 0.9535

P-Value = 0.0465

critical value for Right tailed test with = 0.05

Critical value = 1.645

Decision:

( test statistics = 1.68) > ( Critical value = 1.645)

test statistics lies in rejection region hence,

Null hypothesis (Ho) is rejected.

Conclusion:

there is enough evidence at the 5% level of significance to support that Shaq has significantly improved his free-throw shooting.