Are Men and Women Equal Talkers? A headline in USA Today proclaimed that “Men, women are equal talker.” The headline referred to a study of the numbers of words that samples of men and women spoke in a day. Data given below are the results from the study. Assume that the data are from two independent normal populations. Number of Words Spoken in a Day Men Women n1 = 121 n2 = 101 x1 = 18000 x2 = 17000 s1 = 2000 s2 = 2500 Use a 10% level of significance, do a hypothesis test to determine whether or not the population variances are the same. (Hint: This is a two detailed F test. You need the conclusion here to make a choice between a pooled or a non-pooled t test for part (b).)
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
2. (20) Are Men and Women Equal Talkers? A headline in USA Today proclaimed that “Men, women are equal talker.” The headline referred to a study of the numbers of words that samples of men and women spoke in a day. Data given below are the results from the study. Assume that the
data are from two independent normal populations.
Number of Words Spoken in a Day
Men Women
n1 = 121 n2 = 101
x1 = 18000 x2 = 17000
s1 = 2000 s2 = 2500
Use a 10% level of significance, do a hypothesis test to determine whether or not the population variances are the same. (Hint: This is a two detailed F test. You need the conclusion here to make a choice between a pooled or a non-pooled t test for part (b).)
(10) Based on your conclusion in part (a), use a 1% level of significance to test the claim that men and women speak the same mean number of words in a day by using critical value approach, which means you need to do a two detailed t test to test whether or not men and women are
equal talkers by comparing the average numbers of words they spoke everyday. Note: In case your conclusion from part (a) is that you will have to do a non-pooled t test here, use the smaller one of n1 − 1 and n2 − 1 as the degree of freedom. Since the degree of freedom is very large
here, instead of using t-table with degee of freedom ∞, you may also use standard normal table (Z table) to find the critical values.
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