The following data was collected from a statistics class based on the social acq

Question

The following data was collected from a statistics class based on the social acquaintance exercise described by Malcolm Gladwell in The Tipping Point. x = 40.43 s = 25.23 n = 35 df = 34 a. Use this data to test whether or not the population mean number of acquaintances differs from 30. Report the hypotheses, test statistic, and P -value. Also state the test decision using the alpha = 0.025 significance level, and summarize your conclusion. Round the test statistic to two decimal places. Use the t -table to find a range for the P -value. If there is no lower limit on the P - value, enter 0 for the lower limit. If there is no upper limit on the P -value, enter 1 for the upper limit. H_0: mu H_a: mu Test statistic: t =

Explanation / Answer

Given that,
population mean(u)=30
sample mean, x =40.43
standard deviation, s =25.23
number (n)=35
null, Ho: =30
alternate, H1: !=30
level of significance, = 0.025
from standard normal table, two tailed t /2 =2.345
since our test is two-tailed
reject Ho, if to < -2.345 OR if to > 2.345
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =40.43-30/(25.23/sqrt(35))
to =2.446
| to | =2.446
critical value
the value of |t | with n-1 = 34 d.f is 2.345
we got |to| =2.446 & | t | =2.345
make decision
hence value of | to | > | t | and here we reject Ho
p-value :two tailed ( double the one tail ) - Ha : ( p != 2.4457 ) = 0.0198
hence value of p0.025 > 0.0198,here we reject Ho
ANSWERS
---------------
null, Ho: =30
alternate, H1: !=30
test statistic: 2.446
critical value: -2.345 , 2.345
decision: reject Ho
p-value: 0.0198

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