A company is willing to renew its advertising contract with a local radio station only if the station can prove that more than 20% of the residents of the city have heard the ad and recognize the company's product. The radio station conducts a random survey of 600 people and only 133 remember the ad.
a) Should the company renew the contract? Report your null and alternative hypothesis, p-value and conclusion.
Ho: p=.2
Ha: p>.2
P-value = .0923
Fail to reject the null since P-value < alpha = .05
There is no significant evidence to suggest that the proportion of residents of
the city have heard the ad and recognize the company's product. Thus, they
should not renew the contract.
b) Explain carefully what your P-value means in this context.
There is a 9.23% chance of having 133 or more of 600 people in a random sample remember the ad if in fact 20% of people do.
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A) Null Hypothesis: P=.2
ReplyDeleteAlternative Hypothesis: P>.2
Z Score = (P-hat - P)/ root((P*(1-P))/n)
(133/600 - .2)/ root((.2*.8)/600)
.0217/ root(.16/600)
.0217/ root(.00027)
.0217/.0163
Z Score = 1.331
normalcdf(1.331,1000)= .0916
P = .0916
Conclusion: Do not reject the null because P>.05.
The company should renew the contract since there is enough evidence to suggest that more than 20% of the residents of the city heard the ad and recognized the company's product.
B)P-value: There is a 9.16% chance that 133 people would remember the company's ad and product if 20% of the residents of the city heard the ad and recognized the company's product.
Jacob H.
a)Fail to reject, little evidence that 20% of people remember ad.
ReplyDeleteb) The chance of seeing 133 people out of 600 remember the ad is 9%, which is significantly large.
Molly
A) Ho: P=.2
ReplyDeleteHa: P>.2
Z Score = 1.331
normalcdf(1.331,1000)= .092
P = .092
Fai to reject the null becuase P>.05.
The company should renew the contract since there is evidence to suggest that more than 20% of the residents heard the ad and recognized the product.
B)P-value: There is a 9.2% chance that 133 people would remember the company's ad
Chelsey
a) Z Score = 1.35
ReplyDeleteP = .089
Do not reject the null hypothesis. There is not strong evidence to suggest that more than 20% of people remembered the ad.
b) The Probability of 133 people, in a survey of 600 people, remembering a specific radio ad is 8.9%, which is largely than the alpha value of .05.
Chad