STAT 201 Section 3, HOMEWORK # 6 Spring 2012-2013

1) Consider the following hypothesis test:H0: 25HA: > 25A sample of 40 provided a sample mean of 26.4. The population standard deviationis 6.a) Compute the value of the appropriate test statistic.b) What is the p-value? (Hint: The p-value does not have to be precise, you canlocate and use its approximate position in a table and compare it with thesignificance level. For example, you can answer by stating that the p-value isbetween 0.005 and 0.010 and then compare it against the significance level.Optionally, in order to obtain precise p-values, you can also use Excel, for whichyou can find examples throughout the lecture slides.)c) At = 0.01, what is your conclusion?d) What is the rejection rule using the critical value? What is your conclusion?2) Consider the following hypothesis test:H0: = 100HA: 100A sample of 65 is used. Identify the p-value and state your conclusion for each of thefollowing sample results. Use = 0.05. (Note: Approximate p-values are sufficient.)a) x = 103 and s = 11.5b) x = 96.5 and s = 11.0c) x = 102 and s = 10.513) The Coca-Cola Company reported that the mean per capita annual sales of itsbeverages in the United States was 423 eight-ounce servings (Coca-Cola Companywebsite, February 3, 2009). Suppose you want to show that annual Coca-Colaproduct consumption is higher than 423 servings in Atlanta, Georgia, the location ofCoca-Colas corporate headquarters. A sample of 36 individual from the Atlanta areashowed a sample mean annual consumption of 460.4 eight-ounce servings with astandard deviation of s=101.9 servings.a) State the appropriate hypotheses.b) Compute the value of the appropriate test statistic.c) What is the p-value? (Note: Approximate p-values are sufficient.)d) Test at = 0.05. What do you conclude?4) According to the 2013 Report Card for Americas Infrastructure issued by theAmerican Society of Civil Engineers (ASCE), more than 24% of Pennsylvaniabridges are structurally deficient. To check the validity of this claim, a recentindependent study on 300 bridges were conducted, which revealed that 64 of themwere structurally deficient.a) Formulate the hypotheses that can be used to test the validity of ASCEs claim.b) What is the p-value for the hypothesis test? (Note: The p-value does not have toprecise, you can locate and use its approximate position in a table and compare itwith the significance level. For precise values, you can optionally use Excel.)c) At = 0.05, should the ASCEs claim be rejected?5) Food and Drug Administration runs the risk of making errors in their drug approvalprocess. With a Type I error, the FDA fails to approve a drug that is safe andeffective. A Type II error means the FDA approves a drug that is not safe andeffective.a) The pharmaceutical companies believe the drug approval process is very strict,i.e., some drugs that are not approved should actually be approved. Based on this,2what are the pharmaceutical companies opinion on the magnitude of Type-I andType-II errors (high or low) and why?b) Consumers believe that the drug approval process is a bit loose, i.e., some drugsin the market are not very effective and have too many side effects and theyshould have not been approved. Based on this, what are the consumer opinion onthe magnitude of Type-I and Type-II errors (high or low) and why?3Standard’Normal’Distribution’Table’NORMDIST(z)’z'(a)’Find’probability’from’z’z00.100.200.300.400.500.600.700.800.901.001.051.101.151.201.251.301.351.401.451.501.551.601.651.701.751.801.851.901.952.002.052.10”NORMSDIST(z)0.50.53980.57930.61790.65540.69150.72570.75800.78810.81590.84130.85310.86430.87490.88490.89440.90320.91150.91920.92650.93320.93940.94520.95050.95540.95990.96410.96780.97130.97440.97720.97980.9821(b)’Find’z’from’probability’zNORMSDIST(z)probz2.152.202.252.302.352.402.452.502.552.602.652.702.752.802.852.902.953.003.103.203.303.403.503.603.703.803.904.004.104.204.304.404.500.98420.98610.98780.98930.99060.99180.99290.99380.99460.99530.99600.99650.99700.99740.99780.99810.99840.99870.99900.99930.99950.99970.99980.99980.999890.999930.999950.999970.9999790.9999870.9999910.9999950.9999970.50.510.520.530.540.550.560.570.580.590.600.610.620.630.640.650.660.670.680.690.700.710.720.730.740.750.760.770.780.790.8000.02510.05020.07530.10040.12570.15100.17640.20190.22750.25330.27930.30550.33190.35850.38530.41250.43990.46770.49590.52440.55340.58280.61280.64330.67450.70630.73880.77220.80640.8416prob0.810.820.830.840.850.860.870.880.890.900.910.920.930.940.950.960.970.9750.9800.9850.9900.9950.9990.99950.99990.999990.9999990.99999990.999999990.999999999’z0.87790.91540.95420.99451.03641.08031.12641.17501.22651.28161.34081.40511.47581.55481.64491.75071.88081.96002.05372.17012.32632.57583.09023.29053.71904.26494.75345.19935.61205.9978