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2. Suppose a new production method will be implemented if a hypothesis test supports the conclusion that the new method reduces the mean operating cost per hour.

a. State the appropriate null and alternative hypotheses if the mean cost for the current production method is $220 per hour.

b. What is the type I error in this situation? What are the consequences of making this error?

c. What is the type II error in this situation? What are the consequences of making this error?

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Joshua Stredder
Joshua StredderLv10
28 Sep 2019

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Related questions

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.

1. A researcher believes that the average size of farms in the U.S. has increased from the 2002 mean of 471 acres. She took a sample of 23 farms in 2011 to test her belief and found a sample mean of 487 acres and a sample standard deviation of 46.9 acres. At a 5% level of significance, test the researcher's claim. What is your conclusion?

2. A study by Hewitt Associates showed that 79% of companies offer employees flexible scheduling. Suppose a researcher believes that in accounting firms this figure is lower. The researcher randomly selects 410 accounting firms and determines that 304 of these firms have flexible scheduling. At a 1% level of significance, does your test show enough evidence to conclude that a significantly lower percentage of accounting firms offer employees flexible scheduling? What is the p-value for this test?

3. The American Lighting Company developed a new light bulb that it believes will last at least 700 hours on average. A test is to be conducted using a random sample of 50 bulbs, and a 1% level of significance. Assume that the population standard deviation is 10 hours. What are the consequences of making a type II error? What is the probability of making a Type II error if the true population mean is 695 hours?

Refer to the example of the Cobb-Douglas production function discussed in class, where the GDP (Y), Total Employment (X2 ), and Stock of Fixed Capital (X3 ), are measured for the output, labor input and capital input, respectively. The following model is fitted and the R output is below. The data are yearly data from 1955 to 1974.

lnY = B1 +B2lnX2 + B3lnX3 + u

a. Interpret the coefficient estimate of B3 specific to this problem.

b. Find the rate of change of Y with respect to the change of X2 , at Y=218506.3 and X2=11152.6, and X3 = 340072.45.

c. Find the estimate of the return to scale parameter. (3 pts.)

d. Is there strong evidence that the GDP is inelastic relative to the stocks of fixed capital? Justify your answer at a=0.05.

e. Test if there is a positive (first order) autocorrelation in the error term using a=0.05 . Make sure to state the null and alternative hypotheses, to provide the values of the test statistic and the critical value(s), and to draw a conclusion. (6 pts.)

Regression output for Problem 3.

> fit<-lm(log(y) ~ log(x2) + log(x3))

> summary(fit)

Call:

lm(formula = log(y) ~ log(x2) + log(x3))

Residuals:

Min 1Q Median 3Q Max

-0.057142 -0.016250 -0.005793 0.023512 0.038739

Coefficients:

Estimate Std. Error t value Pr(>|t|)

(Intercept) -1.65233 0.60619 -2.726 0.0144 *

log(x2) 0.33972 0.18569 1.830 0.0849 .

log(x3) 0.84600 0.09335 9.063 6.42e-08 ***

Signif. codes: 0 0.001  0.01 0.05  0.1  1

Residual standard error: 0.02829 on 17 degrees of freedom

Multiple R-squared: 0.9951, Adjusted R-squared: 0.9945

F-statistic: 1719 on 2 and 17 DF, p-value: < 2.2e-16

Durbin-Watson Statistic = 0.425618

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