1. Ten randomly selected groceries in San Francisco has an average sales of 41 thousand dollars every 6 months with a standard deviation of 5.2 thousand dollars. Is this enough evidence to conclude that the groceries are not selling an average of 42 thousand dollars every 6 months? Test the hypothesis at a level of significance of 5%. Use a one-tailed test. 2. A certain manager wishes to find out if the proposed system of operations increases the gross sales of the products of the compared with existing system. To compare the results, six branches for each system are randomly selected for assessment. The result is as follows: Proposed system Existing system Average sales in million 42.5 32.6 Standard deviation 5.7 4.8 Number of branches 6 6 Is the proposed system significantly better than the existing system? Test at a = 0.01 and use a one-tailed test. 3. Oil wells in a large field produce an average of 33.5 barrels per day. Fifteen randomly selected oil wells produce an average of 30 barrels of crude oil per day with a standard deviation of 3.5 barrels. Is this enough evidence to conclude that the oil wells are not producing an average of 335 barrels of crude oil per day? Test at a = 0.1. Use a two-tailed test.
Test the hypothesis of the following problems using the steps.
1. Ten randomly selected groceries in San Francisco has an average sales of 41 thousand dollars every 6 months with a standard deviation of 5.2 thousand dollars. Is this enough evidence to conclude that the groceries are not selling an average of 42 thousand dollars every 6 months? Test the hypothesis at a level of significance of 5%. Use a one-tailed test.
2. A certain manager wishes to find out if the proposed system of operations increases the gross sales of the products of the compared with existing system. To compare the results, six branches for each system are randomly selected for assessment. The result is as follows:
| Proposed system | Existing system | |
| Average sales in million | 42.5 | 32.6 |
| Standard deviation | 5.7 | 4.8 |
| Number of branches | 6 | 6 |
Is the proposed system significantly better than the existing system? Test at a = 0.01 and use a one-tailed test.
3. Oil wells in a large field produce an average of 33.5 barrels per day. Fifteen randomly selected oil wells produce an average of 30 barrels of crude oil per day with a standard deviation of 3.5 barrels. Is this enough evidence to conclude that the oil wells are not producing an average of 335 barrels of crude oil per day? Test at a = 0.1. Use a two-tailed test.
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