Question

Men of few words? Reasearchers claim that women speak significantly more words per day than men. One estimate is that a woman uses about 20,000 words per day, whereas a man uses about 7,000. To investigate such claims, one study used a special device to record the conversations of male and female university students over a four-day period. (Matthias R. Mehl et al., ”Are women really more talkative than men?,” Science, 317 (2007), p. 82) Here are the daily word counts for 19 men in the study:

28408 10084 15931 21688 13182 10575 12880 11071 17799 4429 8918 6495 8153 7015 5255 10054 3998 12639 10974

a. Examine these data for shape, centre, spread, and outliers. The distribution is symmetric enough that use of t procedures is safe.

b. Assume that these observations represent a random sample from this university. Do the data give convincing evidence that the mean number of words per day of men at this university differs from 7000? Use both a confidence interval and P-value to justify your conclusion. Be sure to state your hypotheses.

Answer 1

Ans a ) using minitab>graph>boxplot

we have

the shape of the data is approximately normal with low varibality and one outlier .The distribution is symmetric enough that use of t.

Ans b )

using minitab>stat>basic stat>one sample t

we have

One-Sample T: data

Test of μ = 7000 vs ≠ 7000

Variable N Mean StDev SE Mean 95% CI T P
data 19 11555 6095 1398 (8617, 14493) 3.26 0.004

let the null and alternative hypothesis is

Ho:μ = 7000

Ha:μ ≠ 7000(two tailed)

using confidence interval: since 95% confidence interval (8617, 14493) do not contain value 7000 so we reject Ho and conclude that mean number of words per day of men at this university differs from 7000.

using P value : since p value is less than 0.05 so we reject Ho and conclude that mean number of words per day of men at this university differs from 7000