When Sloan finally ran the study, she collected responses from 800 customers. Out of those 800, 356 said that they had plans to buy a bicycle in the next 5 years. Calculate the 95% confidence interval for the proportion of customers planning to buy a bicycle in the next 5 years, and interpret your answer in context. Show all the steps of your calculations, with clear justification where necessary, and include any formulas used. Round the number at each step to 3dp.

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When Sloan finally ran the study, she collected responses from 800 customers. Out of those 800, 356
said that they had plans to buy a bicycle in the next 5 years.
Calculate the 95% confidence interval for the proportion of customers planning to buy a bicycle in
the next 5 years, and interpret your answer in context. Show all the steps of your calculations, with
clear justification where necessary, and include any formulas used. Round the number at each step
to 3dp.
Transcribed Image Text:When Sloan finally ran the study, she collected responses from 800 customers. Out of those 800, 356 said that they had plans to buy a bicycle in the next 5 years. Calculate the 95% confidence interval for the proportion of customers planning to buy a bicycle in the next 5 years, and interpret your answer in context. Show all the steps of your calculations, with clear justification where necessary, and include any formulas used. Round the number at each step to 3dp.
Armed with some preliminary results for the recently released new bicycle, Sloan is planning a bigger
study about the reception of the new product with 800 customers. Kiloton has a database of
customers that purchased their products before. Sloan will randomly choose customers from the
database and will ask them to rate the new bicycle on a scale from 1-100 and indicate their intention
of buying a bicycle from Kiloton.
As the deadline for the report is soon, Sloan wants to understand what kind of response rate she will
probably get. From the data available from previous surveys taken over the last 10 years, Sloan
determines that, on average, 45 customers reply to the survey per day.
Can we use the Normal approximation to estimate the probability that on any given day there will be
more than 100 replies? Note that you don't need to estimate the probability. You should provide a
justification for whether we can or cannot use the approximation.
Transcribed Image Text:Armed with some preliminary results for the recently released new bicycle, Sloan is planning a bigger study about the reception of the new product with 800 customers. Kiloton has a database of customers that purchased their products before. Sloan will randomly choose customers from the database and will ask them to rate the new bicycle on a scale from 1-100 and indicate their intention of buying a bicycle from Kiloton. As the deadline for the report is soon, Sloan wants to understand what kind of response rate she will probably get. From the data available from previous surveys taken over the last 10 years, Sloan determines that, on average, 45 customers reply to the survey per day. Can we use the Normal approximation to estimate the probability that on any given day there will be more than 100 replies? Note that you don't need to estimate the probability. You should provide a justification for whether we can or cannot use the approximation.
Expert Solution
Step 1

As per our guidelines, we are allowed to answer first question. Thanks

Total customers , n = 800 customers

Number of people who said they had plans to buy a bicycle in next 5 years = X = 356

The sample proportion is calculated as :

p^=XN=356800=0.445 \hat p = \displaystyle \frac{X}{N} = \displaystyle \frac{356}{800} = 0.445

Significance level = α=0.05\alpha = 0.05

Critical value =  zc=z1α/2=1.96z_c = z_{1-\alpha/2} = 1.96

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