Question

6) A marketing survey involves product recognition in New York and California. Of 560 New Yorkers surveyed, 195 knew the product while 195 out of 600 Californians knew the product. a. Construct a 90% confidence interval. b. At the 0.05 significance level, test the claim that the recognition rates are the same in both states.

Answer 1

ANSWER::

(OR)   

a) Constucting the 90% confidence interval

The confidence interval is given as

Where za   is critical value obtained from z-table..

From the normal distribution table  we find that the critical value is 1.645.

The lower confidence bound is given as

=

==  

SImilarly upper bound will be

=

==  

The 90% confidence interval is given as

[   -0.02308569 ,   0.06951429 ]

Rounding off we get

[ -0.0231 , 0.0695 ]

b) Test the claim

The null hypothesis is given as

vs the alternative hypothesis is given as

The pooled sample proportion is given as

=  0.3362069

The test statistic is given as

=

Now obtaining the p-value for two tailed hypothesis

Since p -value > 0.05

We failed to reject the null hypothesis.

There is suffiecient evidence to conclude that the recognition rate are the same in both states.

NOTE:: I HOPE THIS ANSWER IS HELPFULL TO YOU......**PLEASE SUPPORT ME WITH YOUR RATING......

**PLEASE GIVE ME "LIKE".....ITS VERY IMPORTANT  FOR,ME......PLEASE SUPPORT ME .......THANK YOU