Question

Listed below are the winning times (in seconds) of women in the 100-meter dash for consecutive summer Olympic games, listed in order by year. Assume that the times are sample data from a larger population. 11.07 11.08 11.06 10.97 10.54 10.82 10.94 10.75 10.93 a. Find the values of the indicated statistics. i. Mean ii. Median iii. Standard deviation iv. Variance v. Range b. What is the level of measurement of the data? c. Are the values discrete or continuous? d. Do the values constitute a simple random sample? e. What important characteristic of the data is not considered when finding the sample statistics? f. Construct a 95% confidence interval estimate of the population mean. Assume that the population has a normal distribution. Can the result be used to estimate winning times in the future? Why or why not? g. Test the claim that the mean winning time is less than 11 sec. Use a 0.05 significance level. What can we conclude about winning times in the future?

Answer 1

(a) Here

mean = 10.9067

Median = 10.94

Standard deviation s= 0.1776

Variance = 0.03155

Range = Maximum - Minimum = 11.08 - 10.54 = 0.54

(b) Here level of measurement of this data is Interval scale.

(c) Here values are continous.

(d) Yes, it consitute a simple random samle.

(e) Here the important characteristic of the data is that sample size is pretty small than population size.

(f) 95% confidence interval = +- t_critical se₀

= 10.9067

se₀ = 0.1776/sqrt(9) = 0.0592

95% confidence interval = +- t_critical se₀ = 10.9067 +- 2.306 * 0.0592 = (10.77, 11.04)

No, the result cannot be used to estimate the winning times in future as the cofidence interval is only for evaluating population mean.

(g) Here as the confidence interval upper limit crosses the value of 11 so at the significance level 0.05, mean winning time is not less than 11 sec.