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 2020 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

(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.

H0:μ=7000 versus H0:μ>7000

H0:μ≠7000H0 versus H0:μ=7000H0

H0:μ<7000H0 versus H0:μ≠7000H0

H0:μ=7000H0 versus H0:μ≠7000H0

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.

A.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.

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

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

D.There is no evidence that the mean number of words per day of men at this university differs from 7000The sample mean indicates they speak more than 7000 words per day.

Answer 1

Given that,
population mean(u)=7000
sample mean, x =12866.7
standard deviation, s =8342.4722
number (n)=20
null, Ho: μ=7000
alternate, H1: μ!=7000
level of significance, α = 0.05
from standard normal table, two tailed t α/2 =2.093
since our test is two-tailed
reject Ho, if to < -2.093 OR if to > 2.093
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =12866.7-7000/(8342.4722/sqrt(20))
to =3.145
| to | =3.145
critical value
the value of |t α| with n-1 = 19 d.f is 2.093
we got |to| =3.145 & | t α | =2.093
make decision
hence value of | to | > | t α| and here we reject Ho
p-value :two tailed ( double the one tail ) - Ha : ( p != 3.145 ) = 0.0053
hence value of p0.05 > 0.0053,here we reject Ho
ANSWERS
---------------
a.
Normally distributed
b.
null, Ho: μ=7000
alternate, H1: μ!=7000
test statistic: 3.145
critical value: -2.093 , 2.093
decision: reject Ho
p-value: 0.0053
we have enough evidence to support the claim that
option:B
B.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.