Complete the mcq:
1 In testing hypotheses, the researcher initially assumes:
the alternative hypothesis is true.
the null hypothesis is true
errors cannot be made
the population parameter of interest is known
2 The rejection and non rejection regions are divided by the:
rejection value
dividing point
critical value
point of no return
3 When a true null hypothesis is rejected, the researcher has committed a:
Type II error
Type I error
rejection error
error in judgment
4 Whenever hypotheses are established such that the alternative hypothesis is ">", then the test is a:
Type I test
two-tailed test
one-tailed test
Type II test
5 If a business researcher has a new theory about buying habits of consumers and wants to test it, the new theory usually is formulated into the:
null hypothesis
alternative hypothesis
critical value
substantive hypothesis
6 Suppose the alternative hypothesis in a hypothesis test is "the population mean is greater than 65". If the sample size is 50 and alpha is .05, the critical value of z is:
1.645
-1.645
1.96
-1.96
7 Suppose you are testing the null hypothesis that a population mean is greater than or equal to 60, against the alternative hypothesis that the population mean is less than 60. The sample size is 64 and alpha is .05. If the sample mean is 58 and the sample standard deviation is 16, the observed z value is:
1.00
1.00
8.00
2.16
8 A business researcher has a theory that the average age of managers in a particular industry is over 35-years-old, and he wants to prove this. In conducting a statistical test on this theory, the null hypothesis would be:
the population mean is < 35
the population mean is 35
the population mean is = 35
the population mean is > 35
9 A two-tailed hypothesis test about the mean is performed. The observed z value is 1.78. If alpha is 0.05, the correct decision would be:
fail to reject the null hypothesis
reject the null hypothesis
take a larger sample
not enough information to make a decision
10 Suppose a business researcher conducts a hypothesis test and the observed z is positive. If the business researcher is conducting a one-tail test in the upper tail instead of a two-tail test, the table value that the researcher uses for the one-tail test would be what compared to the positive table value for the two-tail test?
The same
Larger
Smaller
None of the above
11
A business researcher has conducted a hypothesis test and obtained an observed z value of 1.47. The p-value for this observed z is:
.0708
.0915
.2138
.4292
12 In performing a hypothesis test where the null hypothesis is that the population mean is 45 against the alternative hypothesis that the population mean is not equal to 45, a random sample of 17 items is selected. The sample mean is 47.6 and the sample standard deviation is 3.3. It can be assumed that the population is normally distributed. The degrees of freedom associated with this are:
2
15
16
17
13 In performing a hypothesis test where the null hypothesis is that the population mean is 6.9 against the alternative hypothesis that the population mean is not equal to 6.9, a random sample of 16 items is selected. The sample mean is 7.1 and the sample standard deviation is 2.4. It can be assumed that the population is normally distributed. The observed "t" value for this problem is:
.05
.20
.33
1.33
14 The diameter of 3.5 inch diskettes is normally distributed. Periodically, quality control inspectors randomly select a sample of 23 diskettes. If the mean diameter of the diskettes is too large or too small the diskette punch is shut down for adjustment; otherwise, the punching process continues. The last sample showed a mean and standard deviation of 3.47 and 0.08 inches, respectively. Using α = 0.01, the appropriate decision is :
reject the null hypothesis and shut down the punch
reject the null hypothesis and do not shut down the punch
do not reject the null hypothesis and shut down the punch
do not reject the null hypothesis and do not shut down the punch
15 A market researcher is testing consumer opinions about a new product. Consumers are asked to rate the product on a scale of from 0 to 10 as to whether or not they would purchase the product if it were available (where 0 = absolutely would not purchase, 10 = absolutely would purchase). Past studies have shown that this scale is normally distributed in the population. The market researcher will not give the go ahead for further development of the product unless the population mean purchase score is greater than 6.00. A sample of eight scores are obtained as follows: 7, 8, 5, 6, 9, 7, 5, 8. The observed t statistic is:
0.21
1.70
1.81
4.83
16 A company believes that it controls more than 40% of the total market share for one of its products. To prove this belief, a random sample of 165 purchases of this product are contacted. It is found that 70 of the 165 purchased this company's brand of the product. If a researcher wants to conduct a statistical test for this problem, the alternative hypothesis would be:
the population proportion is not equal to 0.40
the population mean is equal to 0.40
the population proportion is less than 0.40
the population proportion is greater than 0.40
17 A bank inspector monitors the default rate on personal loans at the AFB member banks. One standard that she examines is that no more than 5% of personal loans should be in default. On each Friday, the default rate is calculated for a sample of 500 personal loans. Last Friday's sample contained 30 defaulted loans. The bank inspector's alternate hypothesis is:
p> 0.05
p< 0.05
p = .05
P ≠ .05
18 A bank inspector monitors the default rate on personal loans at the AFB member banks. One standard that she examines is that no more
than 5% of personal loans should be in default. On each Friday, the default rate is calculated for a sample of 500 personal loans. Last Friday's sample contained 30 defaulted loans. If the bank inspector uses hypothesis testing techniques to test this and if alpha is .10, then the observed value is:
-1.03
1.03
-0.046
0.046
19 Management at a large company has recently implemented a more participatory management style. Management believes that at least half of the company's employees feel that they are more a part of the decision making process than before. To test this, the company's business researcher randomly polls 180 company employees. One hundred and seven of those polled say that they feel they are more a part of the decision making process than before. Suppose the researcher is using a 1% level of significance. The observed value is:
2.67
2.53
1.84
1.56
20 A business researcher is testing the following hypotheses using a 1% level of significance. A sample of 671 is taken and the sample proportion is .38. The critical z value and observed z value are respectively:
2.575, 3.33
2.575, 3.11
2.33, 3.33
2.33, 3.11
21 Suppose a business researcher wants to test the following hypotheses: The researcher takes the following random sample from the population to conduct the test and assumes that the data come from a normally distributed population:
32 35 33 36 35 29
What is the observed value of chi-square for this hypothesis test?
3.33
7.12
11.04
14.23
22 The Electrorist company manufactures a line of electrical resistors. Presently, the carbon composition line is producing 100 ohm resistors. The population variance of these resistors "must not exceed 3 sq. inches" to conform to industry standards. Periodically, the quality control inspectors check for conformity by randomly select 15 resistors from the line and calculating the sample variance. The last sample had a variance of 4.36. Using α = 0.05, the observed value of chi-square is.
29.57
21.80
20.35
19.76
23 The human resources director of American First Banks (AFB), is reviewing the employee training programs of AFB banks. Based on a recent census of personnel, he knows that the variance of teller training time in the Southeast region is 8, and he wonders if the variance in the Southwest region is the same number. His staff randomly selected personnel files for 9 tellers in the Southwest Region, and determined that their mean training time was 25 hours and that the standard deviation was 4 hours. Using α = 0.10, the appropriate decision is:
increase the sample size
reduce the sample size
do not reject the null hypothesis
reject the null hypothesis
24 A business researcher is conducting a one-tailed hypothesis test of the mean. The alternative hypothesis is that the mean is less than 27. A random sample of 36 is taken to test the hypothesis. The sample mean is 26 and the standard deviation is 5. Using an alpha of .05, the business researcher fails to reject the null hypothesis. If the population mean is actually 25, what is the probability of committing a type II error?
.1390
.1745
.2236
.2761
25 A business researcher is testing to determine if a population proportion is more than .38. She takes a random sample of 480 and obtains a sample proportion of .40. Using an alpha of .10, if she decides to fail to reject the null hypothesis but the population proportion is actually .42, what is the probability of committing a type II error?
.0916
.1985
.3015
.6985