Question

Researchers claim that women speak significantly more words per day than men. One estimate is that a woman uses about 20,000 words per day while 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. From these recordings, the daily word count of the 20 men in the study was determined. The table contains their daily word counts. 28,408 10,084 15,931 21,688 37,786 10,575 12,880 11,071 17,799 13,182 8,918 6,495 8,153 7,015 4,429 10,054 3,998 12,639 10,974 5,255 To access the complete data set, click the link for your preferred software format: Excel Minitab JMP SPSS TI R Mac-TXT PC-TXT CSV CrunchIt!

(a) Use the software of your choice to make a histogram of the data.

What value should we remove from the data to make it reasonable to use the t procedures (assume these men are an SRS of all male students at this university)?

value to remove:

(b) With this value removed, carry out a test of significance to determine if the mean number of words per day of men at this university differs from 7000 . (If you're using CrunchIt for your calculations, adjust the default precision under Preferences as necessary. See the instructional video on how to adjust precision settings.)

Choose the correct hypotheses to test. H 0 : μ = 7000 versus H 0 : μ > 7000 H 0 : μ ≠ 7000 versus H 0 : μ = 7000 H 0 : μ < 7000 versus H 0 : μ ≠ 7000 H 0 : μ = 7000 versus H 0 : μ ≠ 7000 With the value removed, find ¯ x . (Enter your answer rounded to two decimal places.) ¯ x = With the value removed, find s . (Enter your answer rounded to three decimal places.) s = With the value removed, find t . (Enter your answer rounded to three decimal places.) t = Using the software of your choice, find the P ‑value. (Enter your answer rounded to four decimal places.) P = What conclusion can we make from this data? Choose the correct answer. There is no evidence that the mean number of words per day of men at this university differs from 7000 The sample mean indicates they speak less than 7000 words per day. There is overwhelming evidence that the mean number of words per day of men at this university differs from 7000 The sample mean indicates they speak more than 7000 words per day. There is overwhelming evidence that the mean number of words per day of men at this university differs from 7000 The sample mean indicates they speak less than 7000 words per day. There is no evidence that the mean number of words per day of men at this university differs from 7000 The sample mean indicates they speak more than 7000 words per day.

Answer 1

(a) value to remove: 37786

(b) H 0 : μ = 7000 versus H 0 : μ ≠ 7000

x = 11,555.16

s = 6,095.015

t = 3.258

P = 0.0044

There is overwhelming evidence that the mean number of words per day of men at this university differs from 7000 The sample mean indicates they speak more than 7000 words per day.

7,000.000	hypothesized value
11,555.16	mean Data
6,095.015	std. dev.
1,398.29	std. error
19	n
18	df
3.258	t
.0044	p-value (two-tailed)