Question
In: Statistics and Probability
A newspaper reported that 48% of smartphone purchases made by people with incomes between $35,000 to...
A newspaper reported that 48% of smartphone purchases made by people with incomes between $35,000 to $50,000 were a certain kind of phone.
(a) If the story is based on a sample of 250 purchases, then should we conclude that this type of phone was getting less than half of the market at that time?
(b) How large a sample is needed for the 95% confidence interval for the population proportion to exclude 50%?
Please show and explain all work.
Solutions
Expert Solution
Answer:
Given that:
A newspaper reported that 48% of smartphone purchases made by people with incomes between $35,000 to $50,000 were a certain kind of phone.
(a) If the story is based on a sample of 250 purchases, then should we conclude that this type of phone was getting less than half of the market at that time?
Under 
the test statistics is
Accept
at
Hence we conclude that this type of phone is getting half of the material
(b) How large a sample is needed for the 95% confidence interval for the population proportion to exclude 50%?
We require 
squaring both sides
we required to 
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