Question

11. Athletes at a local college have a long-term graduation rate of 65%. Over the past several years, a random sample of 38 athletes at the school showed that 17 eventually graduated. We would like to determine whether this indicates that the population proportion of athletes who graduate from this college is now less than 65%. Use a 5% level of significance. a) State the null and alternate hypotheses. b) What sampling distribution will you use? c) Compute the value of the sample test statistic, d) Find the P-value. e) Based on your answers above, will you reject or fail to reject the null hypothesis? f) Interpret your conclusion in the context of this problem.

Answer 1

1a] NULL HYPOTHESIS H0:

ALTERNATIVE Hypothesis Ha:

B] We will use standard normal distribution.

c] test statistic= p(hat)-p/SQRT (p*q/n)

p(hat)= x/n= 17/38= 0.45

Z= 0.45-0.65/sqrt (0.65*0.35/38)

Z= -0.2/0.077

Z= -2.597

d] The P-Value is .0047.The result is significant at p < .05.

e] Decision: REJECT NULL HYPOTHESIS H0

f] We have sufficient evidence to conclude that proportion less than 0.65.

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