Question

A student took a random sample of 173 properties to examine how much more waterfront property is worth. Her summaries and boxplots of the two groups of prices are shown. Construct and interpret a 98% confidence interval for the mean additional amount that waterfront property is 800 worth 600 400 200 Non-Waterfront Pro Waterfront Pro 105 230,106.22 94,838.33 68 326,740.59 157,407.18 The 98% confidence interval is □ □ (Round to the nearest whole number as needed.) Interpret the confidence interval A. We're 98% confident that a。B. We're 98% confident that a。C. We're 98% confident that waterfront property is worth $46,469 to $146,799 more waterfront property is worth $46,469 to $146,799 less houses are worth between $46,469 to $146,799

Answer 1

let sample an sample be water front and not waterfront resp.

Level of Significance ,    α =    0.02
      
mean of sample 1,    x̅1=   326740.59
standard deviation of sample 1,   s1 =    157407.18
size of sample 1,    n1=   68
      
mean of sample 2,    x̅2=   230106.22
standard deviation of sample 2,   s2 =    94838.33
size of sample 2,    n2=   105

$df=\frac{\left ( \frac{s_{1}^{2}}{n_{1}}+\frac{s_{2}^{2}}{n_{2}} \right )^{2}}{\frac{\left ( s_{1}^{2}/n_{1} \right )^{2}}{n_{1}-1}+\frac{\left ( s_{2}^{2}/n_{2} \right )^{2}}{n_{2}-1}}= 98$

t-critical value =    t α/2 =    2.365   (excel formula =t.inv(α/2,df)
          
          
          
std error , SE =    √(s1²/n1+s2²/n2) =    21214
margin of error, E =    t*SE =    50165
          
difference of means =    x̅1-x̅2 =    96634

98% confidence interval is 96634 ± 50165

confidence interval is           
Interval Lower Limit=   (x̅1-x̅2) - E =    46469
Interval Upper Limit=   (x̅1-x̅2) + E =    146799

since, confidence interval is positive,

so, answer is option A)