Fifteen people were asked to indicate their preference for d

Fifteen people were asked to indicate their preference for domestic versus imported cars. The following data showed their preferences.

                        Individual      Domestic vs. Imported

                               1                             +

                               2                             +

                               3                             -

                               4                             +

                               5                             +

                               6                             +

                               7                             -

                               8                             +

                               9                             +

                              10                             +

                              11                             +

                              12                             +

                              13                             +

                              14                             +

                              15                             -

With a = 0.05, test for a significant difference in the preferences for cars. A \"+\" indicates a preference for imported cars.

Solution

So the data set has 15 sample size
indicating + with 1 and - with 0
Our data set becomes
110111011111110 seperate by commas if you get confused.
there are total of 12 1\'s and 3 0\'s
hence P(1) = 12/15 = 4/5 = 0.8
P(0) = 3/15 = 1/5 = 0.2
==>mean = 0.5
sd = 0.212
given alpha = 0.05
=> from tables z = 1.96
Hence error = z*sd/ root n = 1.96*0.212/sqrt(15)=0.107
We have Ho > 0.5
and Ha <= 0.5
Hence a two tailed test
there fore
significance test
==> E = 0.107 <0.5
Hence reject the alternate hypothesis.