Question

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Women athletes at the a certain university have a long-term graduation rate of 67%. Over the past several years, a random sample of 37 women athletes at the school showed that 20 eventually graduated. Does this indicate that the population proportion of women athletes who graduate from the university is now less than 67%? Use a 1% level of significance. (a) What is the level of significance? 0.01 State the null and alternate hypotheses. Ho: p = 0.67; Hi: p < 0.67 O Ho: p = 0.67; HỆ: p + 0.67 Ho: p = 0.67; Hi: p > 0.67 Ho: p < 0.67; Hi: p = 0.67 (b) What sampling distribution will you use? O The Student's t, since np > 5 and ng > 5. The Student's t, since np < 5 and ng < 5. The standard normal, since np > 5 and ng > 5. O The standard normal, since np < 5 and ng < 5. What is the value of the sample test statistic? (Round your answer to two decimal places.) -1.54 x (c) Find the P-value of the test statistic. (Round your answer to four decimal places.) 0.06178 X Sketch the sampling distribution and show the area corresponding to the P-value.

Answer 1

Ans - p= '67 , n= 37 p=20 = 0.54 37 Standard enna (SE) P(1-P) 0.077 .67×(1-'67) 37 test statistic ²-P SE .54-67 077 -1.69 (C) using standard normal distribution, P(z<-169) .0455 10455 -169 Since 0455 > .01(a), so the null hypothesis cannot be rejected Thus there is not enough evidence to say population proportion is less them 676