1. A new breakfast cereal is test-marketed for 1 month at stores of a large supermarket chain. The results for a sample of 16 stores indicate average sales of $1,200 with a standard deviation of $180. Assuming a normal distribution set up a 95% confidence interval estimate of the true average sales of this new breakfast cereal (see the last page for the solutions). State the meaning of µ first, and then interpret the interval; you may use the TI-84 t interval option. 2. If the mean sales of the new cereal are at least $1000 per month, the stores will start selling the cereal for a one-year trial. Should the new cereal get its chance in the cereal aisle for a one-year trial? Explain. 3. A machine being used for packaging seedless golden raisins has been set so that on average, 15 ounces of raisins will be packaged per box. The quality control engineer wishes to test the machine setting and selects a sample of 30 consecutive raisin packages filled during the production process. Their weights are recorded as follows: 15.2 15.3 15.1 15.7 15.3 15.0 15.1 14.3 14.6 14.5 15.0 15.2 15.4 15.6 15.7 15.4 15.3 14.9 14.8 14.6 14.3 14.4 15.5 15.4 15.2 15.5 15.6 15.1 15.3 15.1 At the 5% level of significance, is there evidence that the mean weight per box is different from 15 ounces? Use the 5-step classical rejection region critical value decision rule for this problem. You may use the TI-84 t-test option to calculate the test statistics (tStat). For the rejection region approach recall that we look up the tcritical on the t table, tα,n-1 for a 1 tail and tα/2,n-1 for a 2 tail test. State the meaning of µ, then list the 5 steps. If you reject Ho, construct a (1-α)% CI for µ, and state what we think µ is now after you reject Ho.
1. A new breakfast cereal is test-marketed for 1 month at stores of a large supermarket chain. The results for a sample of 16 stores indicate average sales of $1,200 with a standard deviation of $180. Assuming a
2. If the
3. A machine being used for packaging seedless golden raisins has been set so that on average, 15 ounces of raisins will be packaged per box. The quality control engineer wishes to test the machine setting and selects a sample of 30 consecutive raisin packages filled during the production process. Their weights are recorded as follows: 15.2 15.3 15.1 15.7 15.3 15.0 15.1 14.3 14.6 14.5 15.0 15.2 15.4 15.6 15.7 15.4 15.3 14.9 14.8 14.6 14.3 14.4 15.5 15.4 15.2 15.5 15.6 15.1 15.3 15.1 At the 5% level of significance, is there evidence that the mean weight per box is different from 15 ounces? Use the 5-step classical rejection region critical value decision rule for this problem. You may use the TI-84 t-test option to calculate the test statistics (tStat). For the rejection region approach recall that we look up the tcritical on the t table, tα,n-1 for a 1 tail and tα/2,n-1 for a 2 tail test. State the meaning of µ, then list the 5 steps. If you reject Ho, construct a (1-α)% CI for µ, and state what we think µ is now after you reject Ho.
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