Question

In: Statistics and Probability

A student survey was completed by 446 students in introductory statistics courses at a large university...

A student survey was completed by 446 students in introductory statistics courses at a large university in the fall of 2003. Students were asked to pick their favorite color from black, blue, green, orange, pink, purple, red, yellow.

(a) If colors were equally popular, what proportion of students would choose each color? (Round your answer to three decimal places.)

(b) We might well suspect that the color yellow will be less popular than others. Using software to access the survey data, report the sample proportion who preferred the color yellow. (Round your answer to two decimal places.)

(c) Is the proportion preferring yellow in fact lower than the proportion you calculated in (a)?

(d) Use software to produce a 95% confidence interval for the proportion of all students who would choose yellow.
(e) How does your confidence interval relate to the proportion you calculated in (a)?

it is strictly below that proportion it contains that proportion     it is strictly above that proportion

Solutions

Expert Solution

(a) There are eight different colors, and 446 sample points. If all colors were equally popular, then all colors will be chosen equally. Hence, each color would be chosen by one-eighth of the students. Hence,

(b) Since the data has not been provided, let us assume that the observed proportion of yellow color is

(c) Here we need to conduct the hypothesis test for whether the observed proportion is less than the value calculated in (a) assuming all colors were equally popular.

As the observed statistic is more negative than the critical value, hence we must reject the null hypothesis, and conclude that the proportion preferring yellow is less than what we would expect, assuming all colors were equally popular.

(d) Here we first need to calculate the standard error of observed proportion, and use that to compute the 95% confidence interval as

(e) Since the higher limit of the confidence interval, viz. 0.10518 is less than 0.125, hence the 95% confidence interval is strictly below the proportion calculated in (a)

Entire working has been described asuming proportion of yellow as 0.08. For any other value from the actual data, same steps can be followed

orchestra answered 2 years ago
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