A cooperative store is interested in knowing whether there is any significant difference between the buying habits or male and female shoppers.samples of 14 males and 16 female shoppers gave the following information: male=62,38,43,79,77,23,11,52,33,41,70,49,69,43. female=93,101,72,118,100,45,68,72,47,83,92,106,63,66,85,81.
What do those numbers mean?
What is your question?
To determine if there is a significant difference between the buying habits of male and female shoppers, you will need to perform a statistical analysis, specifically a hypothesis test. In this case, we can use a two-sample t-test to compare the means of the two groups.
Here's how you can conduct the analysis step-by-step:
1. Define the null and alternative hypotheses:
- Null hypothesis (H0): There is no significant difference between the buying habits of male and female shoppers.
- Alternative hypothesis (Ha): There is a significant difference between the buying habits of male and female shoppers.
2. Calculate the means of both male and female shoppers:
- The mean of the male shoppers is: (62 + 38 + 43 + 79 + 77 + 23 + 11 + 52 + 33 + 41 + 70 + 49 + 69 + 43) / 14
- The mean of the female shoppers is: (93 + 101 + 72 + 118 + 100 + 45 + 68 + 72 + 47 + 83 + 92 + 106 + 63 + 66 + 85 + 81) / 16
3. Calculate the standard deviations of each group:
- The standard deviation of the male shoppers can be calculated using the formula: sqrt(((x1 - mean)^2 + (x2 - mean)^2 + ... + (x14 - mean)^2) / (n1 - 1))
- The standard deviation of the female shoppers can be calculated using the same formula with the respective values.
4. Calculate the test statistic:
- The t-test statistic for two independent groups is calculated using the formula: (mean1 - mean2) / sqrt((sd1^2 / n1) + (sd2^2 / n2))
- In this formula, mean1 and mean2 are the means of male and female shoppers, sd1 and sd2 are the standard deviations, and n1 and n2 are the respective sample sizes.
5. Calculate the degrees of freedom:
- The degrees of freedom for the t-test is calculated using the formula: (n1 - 1) + (n2 - 1)
6. Determine the critical value or p-value:
- Find the critical value for the desired level of significance (e.g., 0.05) and the degrees of freedom. Alternatively, you can calculate the p-value associated with the test statistic.
7. Make a decision and interpret the results:
- If the test statistic is larger than the critical value or the p-value is less than the significance level, reject the null hypothesis. This indicates that there is a significant difference between the buying habits of male and female shoppers.
- If the test statistic is smaller than the critical value or the p-value is greater than the significance level, fail to reject the null hypothesis. This suggests that there is no significant difference between the buying habits of male and female shoppers.
Please note that the accuracy of the statistical analysis may be affected by factors like the representativeness of the samples and any underlying assumptions of the test.