Question

In: Statistics and Probability

6) A marketing survey involves product recognition in New York and California. Of 560 New Yorkers...

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.

Expert Solution

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.

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orchestra answered 2 years ago

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