Assignment:
Q1. Consider the following hypothesis test:
Ho:µ ≥ 45
H :µ < 45
A sample of 36 is used. Identity the p-value and state your conclusion for each of the following sample results. Use a = .01
a. x = 44 and s = 5.2
b. x = 43 and s = 4.6
c. x = 46 and s = 5.0
Q2. The Employment and Training Administration reported the U.S. mean unemployment insurance benefit of $238 per week. A researcher in the state of Virginia anticipated that sample data would show evidence that the mean weekly unemployment insurance benefit in Virginia was below the national level.
A. Develop appropriate hypotheses such that rejection of H will support the researcher's contention º
B. For a sample of 100 individuals, the sample mean weekly unemployment insurance benefit was $231 with a sample standard deviation of $80. What is the p-value.
C. At a = 5, what is your conclusion?
D. Repeat the preceding hypothesis test using the critical value approach.
Q3. The cost of a one carat VS2 clarity. H color diamond from Diamond Source USA is $5600. A Midwestern jeweler makes calls to contacts in the diamond district of New York City to see whether the mean price of diamonds there differs from $5600.
a. Formulate hypotheses that can be used to determine whether the mean price in New York City differs from $5600.
b. A sample of 25 New York City contacts provided the prices shown in the CD file
named Diamonds. What is the p-value?
c. At a = .05 can the null hypothesis be rejected? What is your conclusion?
d. Repeat the preceding hypothesis test using the critical value approach.
| Price |
| 4620 |
| 6210 |
| 5150 |
| 5250 |
| 4840 |
| 6320 |
| 5450 |
| 5620 |
| 6140 |
| 5850 |
| 5640 |
| 6575 |
| 5940 |
| 5850 |
| 5825 |
| 5820 |
| 6850 |
| 6010 |
| 5960 |
| 5980 |
| 6330 |
| 5990 |
| 5995 |
| 6360 |
| 5300 |
Q4. Callaway Golf Company's new forged titanium ERC driver has been described as "illegal" because it promises driving distances that exceeded the USGA's standard. Golf Digest compared actual driving distances with the ERC driver and a USGA-approved driver with a population mean driving distance of 280 yards. Based on nine test drives, the mean driving distance by the ERC driver was 286.9 yards. Answer the following questions assuming a sample standard deviation driving distance of 10 yards.
A. Formulate the null and alternative hypotheses that can be used to determine whether the new ERC driver has a population mean driving distance greater than 280 yards.
B. On average, how many yards farther did the golf ball travel with the ERC driver?
C. At a = .05 what is your conclusion?
Q5. Consider the following hypothesis test:
Ho : p = .20
Ha : p ≠ 20
A sample of 400 provided a sample proportion p = .175
a. Compute the value of the test statistic.
b. What is the p-value?
c. At a = .05, what is your conclusion?
d. What is the rejection rule using the critical value? What is your conclusion?
Q6. The Heldrich Center for Workforce Development found that 40% of Internet users received more than 10 e-mail messages per day. A similar study on the use of e-mail was repeated in 2002.
A. Formulate the hypotheses that can be used to determine whether the proportion of Internet users receiving more than 10 e-mail messages per day increased.
B. If a sample of 425 Internet users found 189 receiving more than 10 e-mail messages per day, what is the p-value?
C. At a = 0.5, what is your conclusion?
| Hourly Wage ($) |
| 17.3193 |
| 14.54249 |
| 16.10766 |
| 11.72024 |
| 15.8772 |
| 15.00951 |
| 16.21041 |
| 15.49937 |
| 14.26166 |
| 13.07963 |
| 13.87339 |
| 14.91047 |
| 9.064013 |
| 16.91709 |
| 14.02051 |
| 14.06948 |
| 14.18472 |
| 12.35932 |
| 13.53088 |
| 16.55021 |
| 13.83554 |
| 14.0184 |
| 13.52561 |
| 14.23591 |
| 16.2605 |
| 14.10768 |
| 14.16094 |
| 13.29025 |
| 15.85463 |
| 16.70826 |
| 14.69609 |
| 16.74435 |
| 14.46192 |
| 14.14472 |
| 15.72077 |
| 15.45445 |
| 18.30848 |
| 14.48656 |
| 16.53529 |
| 14.53728 |
| 15.44269 |
| 14.99263 |
| 15.16722 |
| 12.82783 |
| 12.90553 |
| 14.35328 |
| 15.61872 |
| 13.91699 |
| 14.76999 |
| 13.64292 |
| 15.79779 |
| 12.9368 |
| 13.3164 |
| 14.98534 |
| 15.52276 |
| 14.45009 |
| 13.72377 |
| 13.23034 |
| 13.582 |
| 15.69851 |
| 15.29084 |
| 15.03014 |
| 16.87196 |
| 16.11465 |
| 13.21765 |
| 16.09379 |
| 14.46083 |
| 13.88508 |
| 13.07182 |
| 15.349 |
| 16.105 |
| 15.9994 |
| 13.82554 |
| 14.71619 |
| 13.89136 |