A marketing company is considering two different versions of a potential ad, and is specifically interested in whether gender has any bearing on whether people like the ad or not. They conduct a focus group consisting of 200 people, and randomly assign participants to view either version A or version B. Afterwards, they recorded the number of people who had a favorable opinion of each version, as shown below. Version A Opinion total Favorable Unfavorable Female 29 21 50 Male 31 19 50 Total 60 40 100 Version B Opinion total Favorable Unfavorable Female 41 9 50 Male 19 31 50 Total 60 40 100 (a) Which type of test should the marketing company do? A. Chi-squared goodness of fit test B. Chi-squared test of independence (b) Compute the expected counts for both tables: (i) Females with a favorable opinion, Version A: Version B: (ii) Females with an unfavorable opinion, Version A: Version B: (c) Comparing these expected counts with the observed counts given in the tables, which version would have a smaller test statistic? A. Version A B. Version B
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
A marketing company is considering two different versions of a potential ad, and is specifically interested in whether gender has any bearing on whether people like the ad or not. They conduct a focus group consisting of 200 people, and randomly assign participants to view either version A or version B. Afterwards, they recorded the number of people who had a favorable opinion of each version, as shown below.
Version A
| Opinion | total | ||
|---|---|---|---|
| Favorable | Unfavorable | ||
| Female | 29 | 21 | 50 |
| Male | 31 | 19 | 50 |
| Total | 60 | 40 | 100 |
Version B
| Opinion | total | ||
|---|---|---|---|
| Favorable | Unfavorable | ||
| Female | 41 | 9 | 50 |
| Male | 19 | 31 | 50 |
| Total | 60 | 40 | 100 |
(a) Which type of test should the marketing company do?
(b) Compute the expected counts for both tables:
(i) Females with a favorable opinion, Version A:
Version B:
(ii) Females with an unfavorable opinion, Version A:
Version B:
(c) Comparing these expected counts with the observed counts given in the tables, which version would have a smaller test statistic?
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