Msc DEVELOPMENT FINANCEMDEF623: QUANTITATIVE METHODS IN DEVELOPMENT FINANCEExercise OneThe manager of a department store is thinking about establishing a new billing system for the store’s credit customers. After a thoroughly financial analysis, she determines that the new billing system will be cost-effective only if the mean monthly account is more than $ 1700. A random sample of 500 monthly accounts is drawn, for which the sample mean is $1780. The manager knows that the accounts are approximately normally distributed with a standard deviation of $ 350. Can the manager conclude at 5% significance level that the new billing system will be cost-effective? (Take ) A monthly income investment scheme exists that promises variable monthly returns. An investor will invest in it only if he is assured of an average $180 monthly income. He has a sample of 300 months’ returns which has a mean of $190 and a standard deviation of $75. Should he or she invest in this scheme? You are the manager of a fast-food restaurant. The business problem is to determine whether the population mean waiting time to place an order has changed in the past month from its previous population mean value of 4.5 minutes. From past experience, you can assume that the population is normally distributed, with a population standard deviation of 1.2 minutes. You select a sample of 36 orders during a one-hour period. The sample mean is 5.1 minutes. Determine whether there is evidence at the 0.05 level of significance that the population mean waiting time to place an order has changed in the past month from its previous population mean value of 4.5 minutes. (Using the p-value approach) A new stockbroker (XYZ) claims that his brokerage fees are lower than that of your current stock broker's (ABC). Data available from an independent research firm indicates that the mean and std-dev of all ABC broker clients are $18 and $6, respectively. A sample of 100 clients of ABC is taken and brokerage charges are calculated with the new rates of XYZ broker. If the mean of the sample is $18.75 and std-dev is the same ($6), can any inference be made about the difference in the average brokerage bill between ABC and XYZ broker? An analyst believe that the average return of all Ghana stock was greater than 4. The sample size of 36 observation with a sample mean of 5 and the population standard deviation is 2. Will the analyst reject the null hypothesis at 5% level of significance? (p-value approach) An analyst believe that the average return of all Ghana stock was less than 4. The sample size of 36 observation with a sample mean of 3 and the population standard deviation is 2. Will the analyst reject the null hypothesis at 5% level of significance? (p-value approach) A monthly income investment scheme exists that promises variable monthly returns. An investor will invest in it only if he is assured of an average $180 monthly income. He has a sample of 300 months’ returns which has a mean of $190 and a standard deviation of $75. Should he or she invest in this scheme at 5% significance level? Jane has just begun her new job as on the sales force of a very competitive company. In a sample of 16 sales calls it was found that she closed the contract for an average value of 108 dollars with a standard deviation of 12 dollars. Test at 5% significance that the population mean is at least 100 dollars. Company policy requires that new members of the sales force exceed an average of 100 dollars per contract during the probation period. Can we conclude that Jane has met this requirement at the significance level of 95%?

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Msc DEVELOPMENT FINANCEMDEF623: QUANTITATIVE METHODS IN DEVELOPMENT FINANCEExercise OneThe manager of a department store is thinking about establishing a new billing system for the store’s credit customers. After a thoroughly financial analysis, she determines that the new billing system will be cost-effective only if the mean monthly account is more than $ 1700. A random sample of 500 monthly accounts is drawn, for which the sample mean is $1780. The manager knows that the accounts are approximately normally distributed with a standard deviation of $ 350. Can the manager conclude at 5% significance level that the new billing system will be cost-effective? (Take ) A monthly income investment scheme exists that promises variable monthly returns. An investor will invest in it only if he is assured of an average $180 monthly income. He has a sample of 300 months’ returns which has a mean of $190 and a standard deviation of $75. Should he or she invest in this scheme? You are the manager of a fast-food restaurant. The business problem is to determine whether the population mean waiting time to place an order has changed in the past month from its previous population mean value of 4.5 minutes. From past experience, you can assume that the population is normally distributed, with a population standard deviation of 1.2 minutes. You select a sample of 36 orders during a one-hour period. The sample mean is 5.1 minutes. Determine whether there is evidence at the 0.05 level of significance that the population mean waiting time to place an order has changed in the past month from its previous population mean value of 4.5 minutes. (Using the p-value approach) A new stockbroker (XYZ) claims that his brokerage fees are lower than that of your current stock broker's (ABC). Data available from an independent research firm indicates that the mean and std-dev of all ABC broker clients are $18 and $6, respectively. A sample of 100 clients of ABC is taken and brokerage charges are calculated with the new rates of XYZ broker. If the mean of the sample is $18.75 and std-dev is the same ($6), can any inference be made about the difference in the average brokerage bill between ABC and XYZ broker?  An analyst believe that the average return of all Ghana stock was greater than 4. The sample size of 36 observation with a sample mean of 5 and the population standard deviation is 2. Will the analyst reject the null hypothesis at 5% level of significance? (p-value approach) An analyst believe that the average return of all Ghana stock was less than 4. The sample size of 36 observation with a sample mean of 3 and the population standard deviation is 2. Will the analyst reject the null hypothesis at 5% level of significance? (p-value approach) A monthly income investment scheme exists that promises variable monthly returns. An investor will invest in it only if he is assured of an average $180 monthly income. He has a sample of 300 months’ returns which has a mean of $190 and a standard deviation of $75. Should he or she invest in this scheme at 5% significance level? Jane has just begun her new job as on the sales force of a very competitive company. In a sample of 16 sales calls it was found that she closed the contract for an average value of 108 dollars with a standard deviation of 12 dollars. Test at 5% significance that the population mean is at least 100 dollars. Company policy requires that new members of the sales force exceed an average of 100 dollars per contract during the probation period. Can we conclude that Jane has met this requirement at the significance level of 95%?

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