The following is sample information. Test the hypothesis that the treatment means are equal. Use the 0.05 significance level.
Treatment 1
Treatment 2
Treatment 3
5
5
6
5
4
6
8
6
6
9
3
5
(b)
What is the decision rule? (Round your answer to 2 decimal places.)
Reject H0 if the test statistic is greater than .
(c&d)
Compute SST, SSE, and SS total and complete an ANOVA table. (Round SS, MS and F values to 3 decimal places.)
Source
SS
df
MS
F
Treatments
Error
Total
| The following is sample information. Test the hypothesis that the treatment means are equal. Use the 0.05 significance level. |
| Treatment 1 | Treatment 2 | Treatment 3 |
| 5 | 5 | 6 |
| 5 | 4 | 6 |
| 8 | 6 | 6 |
| 9 | 3 | 5 |
| (b) | What is the decision rule? (Round your answer to 2 decimal places.) |
| Reject H0 if the test statistic is greater than . |
| (c&d) | Compute SST, SSE, and SS total and complete an ANOVA table. (Round SS, MS and F values to 3 decimal places.) |
| Source | SS | df | MS | F |
| Treatments |
|
|
|
|
| Error |
|
|
| |
| Total |
|
| ||
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Related questions
| A sample of 42 observations is selected from one population with a population standard deviation of 3.1. The sample mean is 101.0. A sample of 52 observations is selected from a second population with a population standard deviation of 4.0. The sample mean is 99.8. Conduct the following test of hypothesis using the 0.04 significance level. |
| H0 : ?1 = ?2 |
| H1 : ?1 ? ?2 |
| (b) | State the decision rule. (Negative amounts should be indicated by a minus sign. Round your answer to 2 decimal places.) |
| The decision rule is to reject H0 if z is outside the interval (, ). |
| (c) | Compute the value of the test statistic. (Round your answer to 2 decimal places.) |
| Value of the test statistic |
| (e) | What is the p-value? (Round your answer to 4 decimal places.) |
| p-value |
*** Please see p. 2 for Question 2 ***
Question 2 (7 points)
The following Excel output shows the outcome of a linear regression of individuals%u2019 wage per hour (in dollars) on the number of years they attended school (in years).
| SUMMARY OUTPUT | ||||||||
| Regression Statistics | ||||||||
| Multiple R | 0.381932619 | |||||||
| R Square | 0.145872525 | |||||||
| Adjusted R Square | 0.144267022 | |||||||
| Standard Error | 4.753758428 | |||||||
| Observations | 534 | |||||||
| ANOVA | ||||||||
| df | SS | MS | F | Significance F | ||||
| Regression | 1 | 2053.22554 | 2053.22554 | 90.8578469 | 5.45998E-20 | |||
| Residual | 532 | 12022.25261 | 22.59821919 | |||||
| Total | 533 | 14075.47815 | ||||||
| Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | Upper 95.0% | ||
| Intercept | -0.745942699 | 1.045403804 | -0.71354504 | 0.475821452 | -2.799566599 | 1.307681201 | 1.307681201 | |
| Years of School | 0.750448943 | 0.078729942 | 9.531938255 | 0.000545998 | 0.595789385 | 0.9051085 | 0.9051085 | |
Part (a) (1 point)
What is the value of the estimated slope %u201Cb%u201D?
Part (b) (2 points)
Interpret the estimated value of the slope (i.e., explain what the number means in this regression).
Part (c) (1 point)
Is the estimate of the slope statistically significant? Please answer %u201Cyes%u201D or %u201Cno%u201D and explain how you can tell.
Part (d) (2 points)
Explain why we want to be able to reject the null hypothesis H0: %u03B2 = 0.
Part (e) (1 point)
How much of the total variation in wages can be explained by individuals%u2019 education?
| 1 | Which of the following statements about Type I and Type II errors is correct | ||||||||
| a | Type I: Reject a true alternative hypothesis. Type II: Do not reject a false alternative. | ||||||||
| b | Type I: Reject a true null hypothesis. Type II: Do not reject a false null hypothesis. | ||||||||
| c | Type I: Reject a false null hypothesis. Type II: Reject a true null hypothesis. | ||||||||
| d | Type I: Do not reject a false null hypothesis. Type II: Reject a true null hypothesis. | ||||||||
| 2 | You are reading a report that contains a hypothesis test you are interested in. The writer of the report writes that the p-value for the test you are interested in is 0.0749, but does not tell you the value of the test statistic. From this information you can: | ||||||||
| a | Not reject the hypothesis at a Probability of Type I error = .05, but reject the hypothesis at a Probability of Type I error = 0.10 | ||||||||
| b | Reject the hypothesis at a Probability of Type I error = .05, and reject at a Probability of Type I error = 0.10 | ||||||||
| c | Not reject the hypothesis at a Probability of Type I error = 0.05, and not reject at a Probability of Type I error = 0.10 | ||||||||
| d | Reject the hypothesis at a Probability of Type I error = .05, but not reject at a Probability of Type I error = 0.10 | ||||||||
| 3 | The random sample below is obtained to test the following hypothesis about the population mean. | ||||||||
| H?: ? ? | 1500 | ||||||||
| H?: ? > | 1500 | ||||||||
| 620 | 1711 | 366 | 2528 | 2678 | 1661 | 442 | 725 | 1938 | |
| 409 | 330 | 2480 | 542 | 369 | 2124 | 549 | 2074 | 1665 | |
| 1873 | 873 | 2143 | 2061 | 1177 | 2509 | 1264 | 2397 | 1523 | |
| 1837 | 1958 | 1041 | 1639 | 2199 | 2232 | 387 | 2270 | 2136 | |
| 1111 | 1883 | 2612 | 2230 | 1597 | 1726 | 694 | 1990 | 1354 | |
| 2090 | 909 | 2128 | 1608 | 747 | 1121 | 2220 | 2390 | 2347 | |
| 1041 | 316 | 655 | 632 | 2064 | 1901 | 532 | 552 | 846 | |
| 2704 | 1410 | 2165 | 1065 | 937 | 1452 | 2539 | 410 | 656 | |
| 1169 | 527 | 809 | 2364 | 2350 | 2210 | 1459 | 2391 | 856 | |
| 2711 | 1985 | 2382 | 2289 | 1927 | 518 | 2177 | 437 | 1151 | |
| 2018 | 1580 | 607 | 2715 | 2188 | 1691 | 1394 | 2610 | 1186 | |
| 695 | 2428 | 2246 | 858 | 2036 | 1681 | 2449 | 1578 | 1971 | |
| 1846 | 1729 | 2389 | 1737 | 1913 | 1863 | 2072 | 2593 | 2287 | |
| 2220 | 2230 | 551 | 458 | 2626 | 2731 | 488 | 2551 | 1736 | |
| 1373 | 307 | 1803 | 2647 | 2679 | 1508 | 1468 | 1443 | 516 | |
| 1002 | 2116 | 2616 | 817 | 2522 | 460 | 1879 | 1999 | 1837 | |
| The level of significance of the test is ? = 0.05. Compute the relevant test statistic. | |||||||||
| This is a(n) _______ (two-tail, upper-tail, lower-tail) test. The test statistic is TS = _______. | |||||||||
| a | Two-tail test | TS = | 1.81 | ||||||
| Do not reject H?: ? ? 1500. Conclude that the population mean is not greater than 1500. | |||||||||
| b | Upper tail test. | TS = | 1.52 | ||||||
| Do not reject H?: ? ? 1500. Conclude that the population mean is not greater than 1500. | |||||||||
| c | Upper tail test. | TS = | 1.81 | ||||||
| Reject H?: ? ? 1500. Conclude that the population mean is greater than 1500. | |||||||||
| d | Lower tail test. | TS = | 1.98 | ||||||
| Do not reject H?: ? ? 1500. Conclude that the population mean is no greater than 1500. | |||||||||
| 4 | Consider the following hypothesis test. | ||||||||
| H?: ? ? | 30 | ||||||||
| H?: ? > | 30 | ||||||||
| A random sample of n = 15 yielded the following observations | |||||||||
| 51 | 38 | 26 | 16 | 28 | |||||
| 57 | 20 | 33 | 35 | 23 | |||||
| 21 | 47 | 56 | 54 | 36 | |||||
| Use ? = | 0.05 | ||||||||
| TS = ______ | CV = ______ | State the decision rule. | |||||||
| a | 1.68 | 1.761 | Do not reject H?. Conclude the mean is not greater than 30. | ||||||
| b | 1.68 | 1.64 | Reject H?. Conclude the mean is greater than 30. | ||||||
| c | 1.847 | 2.145 | Do not reject H?. Conclude the mean is not less than 30. | ||||||
| d | 1.847 | 1.761 | Reject H?. Conclude the mean is less than 30. | ||||||
| 5 | In a recent study, a major fast food restaurant had a mean service time of 165 seconds. The company embarks on a quality improvement effort to reduce the service time and has developed improvements to the service process. The new process will be tested in a sample of stores. The new process will be adopted in all of its stores, if it reduced mean service time by more than 45 seconds compared to the current mean service time. To perform the hypothesis test, the sample of 48 stores yields the following data (seconds). | ||||||||
| 90 | 96 | 133 | 108 | 136 | 110 | 119 | 138 | ||
| 129 | 98 | 101 | 92 | 135 | 124 | 115 | 90 | ||
| 132 | 125 | 110 | 124 | 126 | 138 | 94 | 130 | ||
| 108 | 96 | 140 | 135 | 102 | 114 | 109 | 137 | ||
| 138 | 104 | 108 | 134 | 92 | 107 | 96 | 119 | ||
| 105 | 111 | 96 | 136 | 126 | 116 | 98 | 131 | ||
| Use ? = | 0.05 | ||||||||
| |TS| = ______ | |CV| = ______ | ||||||||
| a | 1.548 | 1.678 | Do not reject H?. The mean service time is not reduced by more than 45 seconds. Do not adopt the new process. | ||||||
| b | 1.871 | 1.678 | Reject H?. The mean service time is reduced by more than 45 seconds. Adopt the new process. | ||||||
| c | 1.871 | 1.640 | Do not reject H?. The mean service time is not reduced by more than 45 seconds. Do not adopt the new process. | ||||||
| d | 1.548 | 1.640 | Reject H?. The mean service time is reduced by more than 45 seconds. Adopt the new process. | ||||||
