Question

Suppose researchers wanted to know about the prevalence of Mountain Dew consumption A study conducted in 2018 collected data on which soft drinks Americans aged 18 to 29 years consumed in the last 4 weeks In that year , 43.60\% of respondents aged 18 to 29 years stated that they drank Mountain Dew within 4 weeks

Q n 3.8 Suppose the 90%confidence interval calculate for these data was (0.406, 0.466). Which of the following would be possible 95%confidence intervals for these same data? Select all that apply

a) 0.368, 0.486 b) 0.426, 0.446 c) 0.382, 0.490 d) 0.382, 0.550

Q n 3.9 Which of the following is a correct interpretation of the confidence level for the interval you were asked to create?

a) Approximately 90% of samples will contain the value of 0.436, the proportion of Americans aged 18 to 29 in the sample who drank Mountain Dew within the last 4 weeks in 2018, in the 90% confidence intervals created from each sample.

b) One can conclude, with 90% confidence, that the proportion of Americans aged 18-29 who consumed Mountain Dew in the last 4 weeks in 2018 is between the values of the confidence interval from the previous problem.

c) In the long run, 90% samples will have a 90% confidence interval that contains the true proportion of Americans aged 18 to 29 years in 2018 who consumed Mountain Dew in the past 4 weeks.

d) On average, 90% of samples will result in a sample proportion of Americans aged 18-29 years who drank Mountain Dew within the last 4 weeks in 2018 between the values of the confidence interval from the previous problem.

Q3.10 Comparing CI to Hypothesis Test 2 Points Again , not the correct confidence interval values that you would calculated suppose the 90 % confidence interval calculated was( 0.406, 0.466) Let's say you wanted to conduct a hypothesis test testing whether a proportion of less than 0.5 ) of Americans aged to 29 in 2018 had Dew in the last 4 weeks . Would you expect the p value to be small or small or large and then explain your reasoning in no more than two sentence

Answer 1

Solution-3.8

95% confidence interval will be wider than 90% confidence interval as z crit is more cmpared to 90%

Z crit for 90%=1.645 and z crit for 95%=1.96

mark

a) 0.368, 0.486

c)0.382, 0.490

d) 0.382, 0.550

Q n 3.9 Which of the following is a correct interpretation of the confidence level for the interval you were asked to create

we apply confidence interval calcuaed from sample to popuation,here population proportion

we are 90% confident that the true popualtion proportion lies within this interval

c) In the long run, 90% samples will have a 90% confidence interval that contains the true proportion of Americans aged 18 to 29 years in 2018 who consumed Mountain Dew in the past 4 weeks

Solution-3.10

Ho:p=0.50

Ha:p<0.50

suppose the 90 % confidence interval calculated was( 0.406, 0.466)

since the 90% confidenc einterval do not contin 0.50

Reject Ho

since we rejected Ho ,p value will be less than 0.10

expect the p value to be small