he restaurant manager is testing the bartender's ability to pour 45 mL of spirits correctly into a mixed drink. The manager has the bartender pour water into 12 shot glasses to test their ability to pour the correct amount of spirits: 48 45 44 43 46 47 42 46 47 45 47 49 Note: The data appears to be approximately normally distributed. Test the bartender's ability to pour 45 mL at the 5% level of significance. T-Distribution Table a. Calculate the sample mean and standard deviation. x̄ = 45.750 Round to three decimal places if necessary s= 0.000 Round to three decimal places if necessary b. Calculate the test statistic. t= 0.000 Round to three decimal places if necessary c. Determine the critical value(s) for the hypothesis test. -2.201 ×2.201 × + Round to three decimal places if necessary d. Conclude whether to reject the null hypothesis or not based on the test statistic. Reject Fail to Reject
Question
he restaurant manager is testing the bartender's ability to pour 45 mL of spirits correctly into a mixed drink. The manager has the bartender pour water into 12 shot glasses to test their ability to pour the correct amount of spirits: 48 45 44 43 46 47 42 46 47 45 47 49 Note: The data appears to be approximately normally distributed. Test the bartender's ability to pour 45 mL at the 5% level of significance. T-Distribution Table a. Calculate the sample mean and standard deviation. x̄ =
45.750 Round to three decimal places if necessary s=
0.000 Round to three decimal places if necessary b. Calculate the test statistic. t=
0.000 Round to three decimal places if necessary c. Determine the critical value(s) for the hypothesis test. -2.201 ×2.201 × + Round to three decimal places if necessary d. Conclude whether to reject the null hypothesis or not based on the test statistic. Reject Fail to Reject
Solution
a. To calculate the sample mean (x̄), you add up all the values and divide by the number of values. In this case, the sum of all the values is 549 and there are 12 values, so the sample mean is 549/12 = 45.75.
To calculate the standard deviation (s), you first subtract each value from the mean, square the result, add up all these squared values, divide by the number of values minus 1 (which is 11 in this case), and then take the square root of the result. Doing this gives a standard deviation of approximately 2.217.
b. The test statistic (t) is calculated by subtracting the population mean (45) from the sample mean (45.75), and then dividing the result by the standard deviation (2.217) divided by the square root of the number of values (which is the square root of 12 in this case). Doing this gives a test statistic of approximately 0.639.
c. The critical value for a two-tailed t-test at the 5% level of significance with 11 degrees of freedom (which is the number of values minus 1) is approximately ±2.201.
d. Since the test statistic (0.639) is less than the critical value (2.201), we fail to reject the null hypothesis. This means that there is not enough evidence to say that the bartender is not pouring 45 mL of spirits correctly.
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