4 Propose a hypothesis about the proportion AND mean of your

4. Propose a hypothesis about the proportion AND mean of your quantitative data. a. Your proportion hypothesis must contain only one number. For example, looking at the Best Actress Ages example in the text, “at least 25% of best actresses are in her 30s”, “more than 30% are older than 30”, or “15% are 35” are acceptable, “between 10% and 30% are 35” is not. i. Calculate the proportion (to which you refer with your proportion hypothesis) of your data. For example, x% of best actresses were in her 30s. ii. Calculate the 95% Confidence Interval for the proportion. b. Your mean hypothesis must also contain only one number. For example “the average is at most 30 years old”, “the average is under 25”, or “the average is not 40” are acceptable, “the average is between 15 and 40” is not. i. Using the sample mean and standard deviation (from #2 above, also see Chapter 3), calculate the 95% Confidence Interval for the population mean

Data:  3, 3, 3,3,3,4,4,4,4,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,7,7,7,7,7,8,9,10,11,11,11, 12

Solution

Data:  3, 3, 3,3,3,4,4,4,4,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,7,7,7,7,7,8,9,10,11,11,11, 12

Mean = 6.06

SD = 2.48

n = 36

z for 95% confidence interval = 1.96

Margin of error = (z*SD)/sqrt(n) = (1.96 *2.48 / sqrt(36)) = 0.81

Confidence Interval:

(6.06 - 0.81 , 6.06+0.81)

= (5.25 , 6.87) Answer