The data below are yields for two different types of corn seed that were used on adjacent plots of land. Assume that the data are simple random samples and that the differences have a distribution that is approximately normal. Construct a​ 95% confidence interval estimate of the difference between type 1 and type 2 yields. What does the confidence interval suggest about farmer​ Joe's claim that type 1 seed is better than type 2​ seed? Type 1 2068 2036 2191 2577 2153 2013 2280 1551   Type 2 2036 1994 2085 2484 2188 1924 2199 1449

A learn-to-type software program claims that it can improve your typing skills. To test the claim and possibly help yourself out, you and eight of your friends decide to try the program and see what happens. Use the table below to construct an 85%85% confidence interval for the true mean change in the typing speeds for people who have completed the typing program. Let Population 1 be the typing speed before taking the program and Population 2 be the typing speed after taking the program. Round the endpoints of the interval to one decimal place, if necessary. Typing Speeds (in Words per Minute) Before After 42 33 41 54 31 50 30 48 41 31 49 52 34 54 48 49 39 48

The Martin County Health Department needs to estimate the proportion of all children in the county aged 19-35 months that are completely up to date with all state-recommended immunizations. The Martin County Health Department found that 88% of a random sample of children in the county aged 19-35 months were completely up to date with all state-recommended immunizations. Find three different confidence intervals - one with sample size 228, one with sample size 402, and one with sample size 658. Assume that 88% of the children each sample are completely up to date with all state recommended immunizations. Observe how the sample size affects the margin of error and subsequently the width of each interval. Report confidence interval solutions using interval notation. Report all solutions in percent form, rounded to two decimal places, if necessary. • When n = 228, the margin of error for a 95% confidence interval is given by When n = • When n = When n = 228, a 95% confidence interval is…

A company that manufactures baseball bats believes that its new bat will allow players to hit the ball 30 feet farther than its current model. The owner hires a professional baseball player known for hitting home runs to hit ten balls with each bat and he measures the distance each ball is hit to test the company's claim. The results of the batting experiment are shown in the following table. Construct a 90 % confidence interval for the true difference between the mean distance hit with the new model and the mean distance hit with the older model. Assume that the variances of the two populations are the same. Let Population 1 be the distances of balls hit with the new model baseball bat and Population 2 be the distances of balls hit with the old model. Round the endpoints of the interval to one decimal place, if necessary. Hitting Distance (in Feet) New Model Old Model 215 234 202 298 224 294 211 246 215 268 248 211 255 226 228 284 247 221 214 259