C. Compute test value D. Make a decision Recycling Approximately 70% of the U.S. population recycles. According to a green survey of a random sample of 250 college students, 184 said that theyrecycled. At a=0.05, is there sufficient evidence to conclude that the proportion of college students who recycle is greater than 70%?Part 1 of 5(a) State the hypotheses and identify the claim.Ho: p= .70 not claimH₁: p.70 claimThe hypothesis test is a one-tailedAlternate Answer:Ho:p=0.7 not claimH₁ :p>0.7 claimThe hypothesis test is a one-tailed test.Part: 1/5Part 2 of 5(b) Find the critical value. Round the answer to at least two decimal places.The critical value istest.XS

a) Suppose p is the true proportion of college students, who recycle.In this scenario, the number of trials is large (>30). The observations are selected randomly and independently. The z-test for a population proportion can be used. It is mentioned that approximately 70% of the U.S. population recycles and it is needed to test whether the proportion of college students, who recycle is greater than 70%. The null and alternative hypotheses are: H0: p = 0.70 (Not claim) H1: p > 0.70 (Claim) The direction of the test is right sided. The test is one tailed. b) The level of significance is α = 0.05. That is, 1 – α = 0.95. Using the EXCEL formula: =NORM.S.INV(0.95), or from standard normal table corresponding to row of 1.6 and column of .04, it is obtained that, P(z ≤ 1.64) = 0.95. The excel output is, The critical value is, zα = z0.05 ≈ 1.64. That is, above the critical value the area under the curve is 0.05 and below the critical value the area under the curve is 0.95. c) Among a random sample of 250 college students 184 said that they recycled. Hence, the sample size is n = 250, and the number of favorable cases is x = 184. The sample proportion is p̂ = x/n = 184/250 = 0.736. The test statistic is: z = (p̂ – p)/ √ [p (1 – p)/n] = (0.736 – 0.70) / √ [(0.70) (1 – 0.70)/250] = 0.036/0.028982753 ≈ 1.24 The test statistic is 1.24. d) Decision rule: If the test statistic value is greater than or equal to the critical value, reject the null hypothesis. Otherwise, fail to reject the null hypothesis. Conclusion: The test statistic value of 1.24, is less than the critical value of 1.64. Hence, fail to reject the null hypothesis. Thus, there is not sufficient evidence to conclude that the proportion of college students, who recycle is greater than 70%, at 5% level of significance.