A random sample of 4,000 U.S. citizens was asked their opinion concerning gun control. A total of 2,600 of the 4,000 citizens in the sample stated that they are in favor of gun control legislation. Perform the calculations needed to determine whether or not it would be appropriate to construct a large-sample confidence interval for the true population proportion (p). What do you conclude (i.e., is it appropriate) and why?
Blog
We want to test the following null and alternative hypothese…
We want to test the following null and alternative hypotheses about a population proportion: Ho: p = 0.20 Ha: p ≠ 0.20 We observe 300 successes in a sample of 1,000 observations. Assume that it is valid to use large-sample procedures in this problem. Calculate the test statistic needed to test the null hypothesis.
The average height cows of a certain breed is 54 inches and…
The average height cows of a certain breed is 54 inches and the standard deviation of the heights is 8 inches. Fifteen percent of the cows are expected to be less than X inches tall. Find the value of X.
The weights of 25 lambs (in pounds) in a flock of sheep are…
The weights of 25 lambs (in pounds) in a flock of sheep are as follows: 68 73 66 76 86 74 61 89 65 90 69 92 76 62 81 63 68 81 70 73 60 87 75 64 82 Construct a stem-and-leaf display using the first digit as the stem and the second digit as the leaf. Based on the stem-and-leaf display, the median for this set of weights is __________ lb.
The following table shows litter sizes for sows in four bree…
The following table shows litter sizes for sows in four breeds of pigs. Yorkshire Landrace Hampshire Duroc 8 9 8 7 10 9 7 8 11 10 8 9 11 10 9 7 9 8 49 46 32 31 – treatment totals 9.8 9.2 8.0 7.5 – sample means The correct degrees of freedom for total, treatments, and error in the Analysis of Variance table for this problem are ____________.
The grades of 8 students on an exam were as follows: Stud…
The grades of 8 students on an exam were as follows: Student Grade 1 66 2 70 3 64 4 88 5 74 6 72 7 87 8 79 Find the standard deviation of the grades of these 8 students.
Suppose that a 94% confidence interval for μ turns out to be…
Suppose that a 94% confidence interval for μ turns out to be (60 inches, 80 inches). To make more useful inferences from the data, it is desired to reduce the width of the confidence interval. What action should we take to reduce the width of the confidence interval?
Assume that a scientist conducts a 2 x 3 factorial experimen…
Assume that a scientist conducts a 2 x 3 factorial experiment. The Analysis of Variance table is shown below: Source df SS MS F Total 17 1.73397 Factor A 1 0.10125 0.10125 23.0375 Factor B 2 0.81195 0.405975 92.3720 A x B 2 0.76803 0.384015 87.3754 Error 12 0.05274 0.004395 Based on this analysis and a significance level of α = 0.05, what should the scientist conclude?
Breeders of the Longhorn breed of cattle select to increase…
Breeders of the Longhorn breed of cattle select to increase the length of the horns (i.e., the distance from the tip of one horn to the tip of the other horn). A Longhorn breeder would like to know the average length of horns found on Longhorn cattle in Texas. A random sample of 144 Longhorn cattle yields a mean horn length of 72 inches and a standard deviation of 15 inches. Estimate the population mean for length of horns of Longhorn cattle in Texas using a 95% confidence interval. What is the correct interpretation of the confidence interval that you derived?
We are interested in estimating the average driving time of…
We are interested in estimating the average driving time of students who commute to Ohio State. How many students who commute need to be included in our sample to order to be 98% confident that the estimated mean driving time will be within 4 minutes of the true population mean driving time if the standard deviation of the driving times is 8 minutes?