In marketing, response modeling is a method for identifying customers most likely to respond to an advertisement. suppose that in past campaigns 18.4% of customers identified as likely respondents did not respond to a nationwide direct marketing campaign. after making improvements to their model, a team of marketing analysts hoped that the proportion of customers identified as likely respondents who did not respond to a new campaign would decrease. the analysts selected a random sample of 1500 customers and found that 252 did not respond to the marketing campaign.

the marketing analysts want to use a one? sample z? test to see if the proportion of customers who did not respond to the advertising campaign, p, has decreased since they updated their model. they decide to use a significance level of ? =0.10.

determine the p? value for this test. give your answer precise to at least three decimal places.

determine the value of the z? statistic. give your answer precise to at least two decimal places.

select the correct null (h0) and alternative (h1) hypotheses.

a. h0: p? =0.184 and h1: p? < 0.184
b. h0: p=0.184 and h1: p? 0.184
c. h0: p? =0.168 and h1: p? < 0.168
d. h0: p=0.184 and h1: p< 0.184
e. h0: p=0.168 and h1: p< 0.168

z=

p-value:

z ≈ -1.60

p-value ≈ 0.055

Explanation:

For a better understanding of the above answer let first explain some terms  

Hypothesis testing

This is a statistical process that involves analyst testing an assumption (i.e. a null hypothesis) concerning a population parameter. It tell the analyst whether or not the hypothesis is true  

Null Hypothesis  

This is an assumed postulate in statistics that states that there is no significance statistically that exists in a set of given observation, this is stating that for a randomly selected value from a sample space that there is no variation between that value and the mean of the sample space  and it is set in opposition to alternative hypothesis. Denoted by H₀

Alternative Hypothesis  

This a postulate in statistics that states that there is a statistical significant relationship between two variables, i.e. this hypothesis is say that there is a variation between a variable and its mean. Denoted by H₁

P-Value

Statistically the p-Value is of values (between 0 and 1) that help determine the significance of a hypothesis test. A p-Value of ≤ 0.05 i.e. a small p-Value shows strong evidence against null hypothesis and hence the null hypothesis would be rejected.  

Significance Level (Alpha)

This can be defined as the probability of discarding or rejecting a null hypothesis when it is actually true.

The step-by-step solution is shown on the uploaded image

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