Question 1 (1 point) Lego is liked by children as well as adults. Management at a lego company wonders if lego sets purchased for adults are on average more expensive than than lego purchased for children (because lego sets liked by adults are often more expensive). So management collects a random sample of 86 lego sets purchased for children and 92 sets purchased for adults (buyers are interviewed). They find that on average, $60 was spent on lego sets purchased for children, with a standard deviation of $19.64. Whereas, lego sets purchased for adults were on average $85 with a standard deviation of $33.56. So management wants to investigate if HA: a - c > 0, where a represents adults and c represents children. What is the standard error for the difference between sample means for money spent on - lego between the adults group and the children group SE(a Yc)? Note: 1- Round your intermediate numbers to 4 decimal places. 2- Round you final answer to 3 decimal places. Enter your final answer to 3 decimal places. Your Answer: A student wants to know if the houses in two different neighborhoods have roughly the same price (in millions of dollars) or not. In other words, she wants to test the following hypotheses: (Ho - Ho: 1 2 = 0 0 #0 HA : 1 - 2 7 0 She takes a random sample of houses from each neighborhood and finds that the summary statistics for the two neighborhoods look as follows. Neighborhood 1 Neighborhood 2 n1 =39 Y1 =$1.4 n2 =22 Y2 =$0.8 |S =$0.37 S =$0.54 Find the t-statistic (test statistic) used to test the hypothesis. Note: 1- Do not round any intermediate numbers. 3- You do not need to change the unit of measure. You can work with the data in ($1,000,000s). 2- Only round your final answer to 3 decimal places. Enter your final answer with 3 decimal places. Question 3 (1 point) Assume you have a t-test for the difference between two means: o 1 2 - = 0 0 HA : 1 - 2 7 0 From a survey, you know that 1 =102, 2 =80, and SE( - Y2) =3.1. After calculating the degree of freedom, you use software to find the corresponding critical value for a 95% confidence interval to be 2.2. Construct the 95% confidence interval for the mean and report the upper limit. Note: 1- Only round your final answer to the nearest integer. Your Answer: Answer Question 4 (1 point) Assume you have a t-test for the difference between two means: 0 Ho 1 : - - 2 = 0 HA: 1 - 20 - From a survey, you know that 1 =99, 2 =79, and SE( Y2) =2.1. After calculating the degree of freedom, you use software to find the corresponding critical value for a 95% confidence interval to be 2.2. Construct the 95% confidence interval for the mean and report the lower limit. Note: 1- Only round your final answer to the nearest integer. Your Answer: Answer Question 5 (1 point) Assume you have a t-test for the difference between two means: H : 1 - 2 =6, 0 HA : - 76. From a survey, you know that 1 =110, 2 =80, n =53, n2 =50, S1 =9, and S2 =9. Find the standard error of the estimated mean difference SE(1 Y2). Note: 1- Only round your final answer to 3 decimal places. Enter your final answer with 3 decimal places. Your Answer: Answer Question 6 (1 point) For larger number of samples (e.g greater than 1000), the t-distribution can be approximated by the normal distribution. True False