Question

1. The production supervisor of an assembly line for producing cheeses suspects that the weight of the bags produced is higher than the specification of 200 g She would like to take a simple random sample of bags of cheeses produced by the assembly line and perform a statistic test to confirm that this is indeed the case. (6 points) a. What would be the null and alternative hypothesis for this research? b. What is the type I error in general and in this situation? c. What is the type Il error in general and in this situation? 2. A simple random sample of 50 accounts is taken from an account receivables portfolio of XYZ Ltd and the average account balance is $650. The population standard deviation o is known to be $70. (6 points) YORKVILLE BUSI 1013 statistics for Business UNIVERSITY a. Test the hypothesis that the population mean account balance is greater than $620 using the p-value approach and a 0.05 level of significance. b. Test the hypothesis that the population mean account balance is less than $800 using the critical value approach and a 0.05 level of significance. c. Test the hypothes is that the population mean account balance is different from $750. using the p-value approach and a 0.05 level of significance. 3. A simple random sample of 70 customers is taken from a customer information file and the average age is 36. The population standard deviation o is unknown. Instead the sample standard deviation s is also calculated from the sample and is found to be 4.5. (6 points) a. Test the hypothes is that the population mean age is greater than 33 using the critical value approach and a 0.05 level of significance. b. Test the hypothes is that the population mean age is less than 38 using the p-value approach and a 0.05 level of significance c. Test the hypothes is that the population mean age is different from 32 using the p-value approach and a 0.05 level of significance. 4. The proportion of customers who are completely satisfied in a recent satisfaction survey of 300 customers at XYC Inc. is found to be 0.26. (6 points) a. Test the hypothesis that the population proportion of customers who are completely satisfied is greater than 0.22 using the critical value approach and a 0.05 level of significance. b. Test the hypothes is that the population proportion of customers who are completely satisfied is less than 0.30 using the p-value approach and a 0.05 level of significance c. Test the hypothes is that the population proportion of customers who are completely satisfied is different from 0.24 using the p-value approach and a 0.05 level of significance. 1. Waiting time for checkout line at two stores of a supermarket chain were measured for a random sample of customers at each store. The chain wants to use this data to test the research (alternative) hypothesis that the mean waiting time for checkout at Store 1 is lower than that of Store 2. (12 points) Store 1 (in Seconds) Store 2 (in Seconds) 461 264 384 308 167 266 293 224 187 244 115 178 195 279 280 289 228 253 315 223 205 197 a. What are the null and alternative hypothesis for this research? b. What are the sample mean waiting time for checkout line and the sample standard deviation for the two stores? c. Compute the test statistic t used to test the hypothesis. Note that the population standard deviations are not known and therefore you cannot use the formula in Section 10.1. Use the one in Section 10.2 instead d. Compute the degree of freedom for the test statistic t e. Can the chain conclude that the mean waiting time for checkout at Store 1 is lower than that of Store 2? Use the critical-value approach and a 0.05 to conduct the hypothesis test. f. Construct a 95% confidence interval for the difference of mean waiting time for checkout line at the two stores. 2. To compare prices of two grocery stores in Toronto, a random sample of items that are sold in both stores were selected and their price noted in the first weekend of July 2018: (12 Points) Difference (Store A-Store B) Store B Item Store A 1 1.65 1.99 0.34 2 8.70 8.49 0.21 YORKVILLE BUSI 1013 statistics for Business UNIVERSITY 3 0.75 0.90 0.15 1.05 0.99 0.06 -0.69 5 11.30 11.99 7.70 7.99 -0.29 -0.44 7 5 6.99 8 3.70 3.59 0.11 -0.39 9 8.60 8.99 10 3.90 4.29 -0.39 a. What are the null and alternative hypothesis if we want to confirm that on average, prices at Store 1 is different from the prices at Store 2, that is, the difference is different from 0? b. What are the sample mean difference in prices and the sample standard deviation? c. Compute the test statistic t used to test the hypothesis. d. Compute the degree of freedom for the test statistict e. Can we conclude that on average, prices at Store 1 is different from the prices at Store 2? Use the critical-value approach and a 0.05 to conduct the hypothesis test. f. Use the above data to construct a 95% confidence interval for the difference in prices between the two stores.

Answer 1

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