Marketing Research Topic 8
An index that is calculated from sample data and whose value determines whether to accept or reject a null hypothesis is a - test statistic - critical value - significance level - decision rule
test statistic
Accepting a null hypothesis when it is false is called a(n) - type I error. - type II error. - hypothesis error. - power of the test. - significance level.
type II error.
Assume you are doing a chi-square test for independence between class and grade. Given the following data collected by sample survey methods, answer the following questions. Class I II Grade A 14 6 B 25 15 C 60 20 D 34 6 E 17 3 If the computed χ2 value for this table was 8.7 and the value from the back of the book with the correct degrees of freedom was 9.49 with α = 0.05 you would - accept the null hypothesis that grade and class are correlated - reject the null hypothesis that grade and class are correlated - accept the null hypothesis that grade and class are independent - reject the null hypothesis that grade and class are independent - it is too close to tell whether to accept or reject
accept the null hypothesis that grade and class are independent
To overcome the problem of the chi-square value being directly proportional to the sample size, the following measure(s) has (have) been developed: - Phi-squared - Contingency coefficient - Cramer's V - Only 1 and 2 - all of the above
all of the above
The basic steps recommended in hypothesis testing, in the correct order, are - analyze data which support an alternative hypothesis or position, conceptualize a null hypothesis, raise the question of the probability that the empirical evidence supporting the original position could have been a statistical accident, calculate the p-value. - estimate a p-value, develop and analyze data, conceptualize a null hypothesis, cluster the data into two testable groups. - conceptualize a null hypothesis, raise the question of the probability that the empirical evidence supporting the original position could have been a statistical accident, develop and analyze data, calculate the p-value. - cluster the data into two or three groups, analyze the data, calculate the p-value, test the null hypothesis. - cluster the data into as many groups as needed, develop and analyze the data, raise the question of the probability that the empirical evidence supporting the original position could have been a statistical accident, calculate the p-value.
conceptualize a null hypothesis, raise the question of the probability that the empirical evidence supporting the original position could have been a statistical accident, develop and analyze data, calculate the p-value.
A subscription service stated that preferences for different national magazines were independent of geographical location. A survey was taken in which 300 respondents randomly chosen from three areas were given a choice among three different magazines. Each person expressed his or her favorite. The following results were obtained: Region Magazine X Magazine Y Magazine Z Total ___________________________________________________________________________________________ New England 75 50 175 300 Northeastern 120 85 95 300 Southern 105 110 85 300 Total 300 245 355 900 Suppose the chi-square value for the above test is 15; this will yield a significance level closest to the value - .1 - .05 - .01 - .005 - .001 - New England 75 50 175 300
.05
Assume you are doing a chi-square test for independence between class and grade. Given the following data collected by sample survey methods, answer the following questions. Class I II Grade A 14 6 B 25 15 C 60 20 D 34 6 E 17 3 What is the probability of making a C and being in class II ? - .05 - .10 - .25 - .40 - .50
.10
Given the following 2 X 2 contingency table Q1 yes no Q2 yes 23 36 59 no 46 15 61 69 51 What would the overall chi-square value be for the whole table if the expected value for the Q1 yes - Q2 yes cell was equal to 23? - 0.0 - 1.0 - 5.0 - 9.9 - some number greater than 10.0
0.0
The criterion (criteria) to use while making the decision to reject or not to reject the null hypothesis is (are) 1. significance level 2. number of degrees of freedom 3. one or two tailed test - 1 - 2 - 3 - 1 and 2 - all of the above
1
The limitation of chi square as an association measure is 1. it is hard to compare cross-tabulations with different sample sizes. 2. it doesn't indicate how the variables are related. 3. it is difficult to obtain a feel for its value (since it has no upper bound). - 1 - 2 - 3 - 1, 2, and 3 - 1 and 2 only
1, 2, and 3
A subscription service stated that preferences for different national magazines were independent of geographical location. A survey was taken in which 300 respondents randomly chosen from three areas were given a choice among three different magazines. Each person expressed his or her favorite. The following results were obtained: Region Magazine X Magazine Y Magazine Z Total ___________________________________________________________________________________________ New England 75 50 175 300 Northeastern 120 85 95 300 Southern 105 110 85 300 Total 300 245 355 900 The number of degrees of freedom is - 4 - 6 - 7 - 9 - none of the above
4
Assume you are doing a chi-square test for independence between class and grade. Given the following data collected by sample survey methods, answer the following questions. Class I II Grade A 14 6 B 25 15 C 60 20 D 34 6 E 17 3 The degrees of freedom for this table is - 1 - 2 - 4 - 5 - 10
4
Two branches of a major multinational corporation conducted surveys to measure the association between income level (low, mid, high) and need for a certain produce (low, mid, high). The sample size in one survey was 100 and in the other, 200. The branches now wish to compare the two cross tabulations that were generated from the surveys. Given this information, the Chi square statistic would provide an easy-to-interpret method to compare the associations. (T/F)
False
In order to reduce the probability of committing a Type II error, the probability of committing a Type I error must necessarily decreased (T/F)
False
The Chi square test cannot be used to ascertain whether the observed pattern fits with the expected pattern. (T/F)
False
The contingency coefficient varies between 0 and 1. The 0 value occurs in the case of no association (i.e., the variables are statistically independent), but the maximum value of 1 is never achieved. (T/F)
False
The larger the degrees of freedom, the lower is the likelihood of observing differences among the variables. (T/F)
False
The null hypothesis associated with the sample Chi square statistic is that the two (intervally scaled) variables are statistically independent. (T/F)
False
The process of hypothesis testing, begins with an assumption about a sample statistic (T/F)
False
Assume you are doing a chi-square test for independence between class and grade. Given the following data collected by sample survey methods, answer the following questions. Class I II Grade A 14 6 B 25 15 C 60 20 D 34 6 E 17 3 What is the expected value of the cell representing a grade of B for class II ? - 5 - 10 - 20 - 40 - 50
10
A subscription service stated that preferences for different national magazines were independent of geographical location. A survey was taken in which 300 respondents randomly chosen from three areas were given a choice among three different magazines. Each person expressed his or her favorite. The following results were obtained: Region Magazine X Magazine Y Magazine Z Total ___________________________________________________________________________________________ New England 75 50 175 300 Northeastern 120 85 95 300 Southern 105 110 85 300 Total 300 245 355 900 If the appropriate null hypothesis for a chi-square test were not rejected, the following would be implied: 1. Subscription for magazine X = subscription for magazine Y = subscription for magazine Z. 2. The probability of magazine preference (unconditional on location) is equal to the probability of magazine preference (conditional on location). 3. Magazine preferences are uncorrelated with location. - 1 - 2 - 3 - 2 and 3 - 1, 2, and 3 - 2. The probability of magazine preference (unconditional on location) is equal to the probability of magazine preference (conditional on location).
2 and 3
New Products Incorporated ran a test market for their latest product in two markets, City A and City B. Both have equal populations. The average weekly sales were $1,000 and $800, respectively, in the two cities. Based on this information, we can say that 1. sales in City A are significantly higher than sales in City B. 2. the difference in the sales level could be due to a sampling error. 3. the difference in the sales level may be due to the fact that the residents of City B accepted the product to a lesser degree than those of City A. - 1 - 2 - 3 - 1 and 3 - 2 and 3 - 2. the difference in the sales level could be due to a
2 and 3
Assume you are doing a chi-square test for independence between class and grade. Given the following data collected by sample survey methods, answer the following questions. Class I II Grade A 14 6 B 25 15 C 60 20 D 34 6 E 17 3 If the expected value for a grade of A for a class II was 3, the cell's chi-square would be - ½ - 1 - 2 - 3 - 9
3
Location (L) Frequency (F) Convenient Not Convenient Row Total ________________________________________________________________________________________ Often 25 15 40 Occasional 55 45 100 Seldom 20 40 60 Column Total 100 100 For the data above, which of the following statements is true? 1. The χ2 statistic is 4.167. 2. The χ2 statistic is 6.25. 3. The p-value is less than 0.01. - 1 - 2 - 3 - 1 and 3 - 2 and 3 - 3. The p-value is less than 0.01.
3
Given the following 2 X 2 contingency table, what would be the expected number of people that said yes to both the questions if your null hypothesis stated that you expected an equal number in all cells? Q1 yes no Q2 yes 23 36 59 no 46 15 61 69 51 - 25 - 30 - 33.9 - 40 - not enough information given to test this hypothesis
30
Hypothesis testing can be used to establish whether the null hypothesis is true or false. (T/F)
False
The Berkeley Supermarket buys its supplies of potatoes from two different farms, A and B. In a recent sampling test, it was found that the sample taken from Farm A had a mean weight of 10 ounces per potato, whereas the sample from Farm B had a mean weight of 10.3 ounces. In view of this test, is there a statistically discernible difference (at the 95 percent confidence level) between the mean weights of the potatoes of the two farms? - Yes. - No, because the difference of 0.3 ounces is very small compared to the mean (approximately 3 percent). - The standard deviations of both samples must be known (the sample sizes are irrelevant) before the above question can be answered. - Both the standard deviations and sample sizes must be known before the above question can be answered. - Even if both the standard deviations and sample sizes were known, the above question cannot be answered.
Both the standard deviations and sample sizes must be known before the above question can be answered.
A high p-value means that the probability of a statistically significant difference is high. (T/F)
False
A high value of b indicates that the test of hypothesis is working very well. (T/F)
False
A major advantage of the Chi square statistic as a measurement of association between two questions is that it is independent of the sample size, making it easy to interpret in an absolute sense. (T/F)
False
The manager of the marketing division of Acme Corporation forecasts an average monthly sales in 1978 of $65,000. In the first seven months of 1978, the average monthly sales were $63,200, with a standard deviation of $500. The management wishes to test the hypothesis Ho that "statistically" the manager was right (Ho:μ = 65,000) against the alternative hypothesis that he was wrong in his forecast (Ho: μ = 65,000), using a two-tail test. Assuming normal distribution of monthly sales, which of the following statements is true? - Ho is rejected at the 5 percent significance level but accepted at - the 1 percent significance level. - Ho is accepted at both the 5 percent and 1 percent significance levels. - Ho is accepted at the 5 percent significance level but rejected at the 1 percent significance level. - Ho is rejected at both the 5 percent and 1 percent significance levels. - None of the above.
Ho is rejected at both the 5 percent and 1 percent significance levels.
A p-value of .45 means that the evidence against the null hypothesis is very weak. (T/F)
True
Assuming the hypothesis to be true, the significance level indicates the percentage of sample means that are outside the cutoff limits. (T/F)
True
Degrees of freedom refers to the number or bits of free or unconstrained data used in calculating a sample statistic. (T/F)
True
If the p-value is less than or equal to 0.05, then it is valid to say that the sample evidence is significant at .05 level. (T/F)
True
The Chi square test can provide a useful measurement of association. (T/F)
True
The higher the significance level used for testing a hypothesis, the higher is the probability of rejecting the null hypothesis when it is true. (T/F)
True
The hypothesis test serves to quantify the reliability of research results, indicating the extent to which the data support the empirical findings. (T/F)
True
The purpose of hypothesis testing is not to question the computed value of the sample statistic but to make a judgment about the difference between that sample statistic and the hypothesized population parameter. (T/F)
True
Type II error occurs when the null hypothesis is not rejected when it is false. (T/F)
True
If the researcher, in making a statistical test, rejects a true hypothesis, the error is called - Type I error - Type II error - Type III error - no error is made - none of the above
Type I error
