Question

Elizabeth Mjelde, an art history professor, was interested in whether the value from the Golden Ratio formula, was the same in the Whitney Exhibit for works from 1900 to 1919 as for works from 1920 to 1942. Thirty-seven early works were sampled, averaging 1.74 with a standard deviation of 0.11. Sixty-five of the later works were sampled, averaging 1.746 with a standard deviation of 0.1064. Do you think that there is a significant difference in the Golden Ratio calculation?

a) Yes, there is a significant difference.

b) No, there is no significant difference.

c) Both a,b,and c

d) None of the above

Answer 1

To determine if there is a significant difference in the Golden Ratio calculation between works from 1900-1919 and works from 1920-1942, we can perform a two-sample t-test.

Step-by-step explanation:

To determine if there is a significant difference in the Golden Ratio calculation between works from 1900-1919 and works from 1920-1942, we can perform a two-sample t-test.

The null hypothesis is that the means of the two samples are equal, while the alternative hypothesis is that the means are different. The t-test compares the means of the samples and calculates a p-value.

1. State the hypotheses:
   • H0: μ1 = μ2 (the means are equal)
   • Ha: μ1 ≠ μ2 (the means are different)
2. Calculate the test statistic and p-value:
   • Collect the necessary information from the problem statement: sample means, sample standard deviations, and sample sizes.
   • Calculate the test statistic: t = (mean1 - mean2) / sqrt((sd1^2 / n1) + (sd2^2 / n2))
   • Calculate the degrees of freedom: df = n1 + n2 - 2
   • Find the p-value by comparing the test statistic to the t-distribution with the appropriate degrees of freedom.
3. Make a decision:
   • If the p-value is less than the significance level (usually α = 0.05), reject the null hypothesis. There is sufficient evidence to suggest that there is a significant difference in the Golden Ratio calculation.
   • If the p-value is greater than the significance level, fail to reject the null hypothesis. There is not enough evidence to suggest a significant difference in the Golden Ratio calculation.
4. State the conclusion:
   • Based on the calculated p-value and the chosen significance level, state whether there is a significant difference in the Golden Ratio calculation.