In a survey of consumers aged 12 and older, respondents were asked how many cell phones were in use by the household. (No two respondents were from the same household) Among the respondents, 208 answered "none", 285 said "one", 358 said "two", 149 said "three", and 129 responded with four or more. A survey respondent is selected at random. Find the Probability that his/her household has four or more cell phones in use. Is it likely for a household to have four or more cell phones in use? Consider and event to be unlikely if its probability is less than or equal to 0.05.

Question
Asked Oct 28, 2019

In a survey of consumers aged 12 and older, respondents were asked how many cell phones were in use by the household. (No two respondents were from the same household) Among the respondents, 208 answered "none", 285 said "one", 358 said "two", 149 said "three", and 129 responded with four or more. A survey respondent is selected at random. Find the Probability that his/her household has four or more cell phones in use. Is it likely for a household to have four or more cell phones in use? Consider and event to be unlikely if its probability is less than or equal to 0.05.

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Expert Answer

Step 1

This question can be solved using hypothesis test for a Proportion. 

Among the respondents, 208 answered "none", 285 said "one", 358 said "two", 149 said "three", and 129 responded with four or more. There are 208+285+358+149+129 = 1129 respondents.

Proportion of respondents that responded with four or more = 129/ 1129 = 0.11426 

Step 2

p=sample proportion

P=Hypoth...

Null Hypothesis: p
0.05
Alternate Hypothesis: p > 0.05
р-P
P (1-P)
0.11426 -0.05
=9.907
Z =
V0.05 (0.95)
1129
Z = 9.907
p-value 1
P-value>0.05
Decision: Fail to reject the null hypothesis
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Null Hypothesis: p 0.05 Alternate Hypothesis: p > 0.05 р-P P (1-P) 0.11426 -0.05 =9.907 Z = V0.05 (0.95) 1129 Z = 9.907 p-value 1 P-value>0.05 Decision: Fail to reject the null hypothesis

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