Discuss the below:
Q1. Mendelian Genetics?When Mendel conducted his famous genetics experiments with peas, one sample of offspring consisted of 428 green peas and 152 yellow peas.
a. Use statdisk to find the following confidence interval estimates of the percentage of yellow peas.
99% confidence interval
98% confidence interval
95% confidence interval
90% confidence interval
b. After examining the pattern of the above confidence intervals, complete the following statement. As the degree of confidence decreases, the confidence interval limits
c. Explain why the preceding completed statement makes sense. Why should the confidence intervals behave as described?
Q2. Internet shopping?In a Gallup poll, 1025 randomly selected adults were surveyed and 29% of them said that they used the Internet for shopping at least a few times a year.
a. Find the point estimate of the percentage of adults who use the Internet for shopping
b. Find a 99% confidence interval estimate of the percentage of adults who use the Internet for shopping
c. Based on the result from part (b), if a traditional retail store wants to estimate the percentage of adult Internet shoppers in order to determine the maximum impact of Internet shoppers on its sales, what percentage of Internet shoppers should be used?
Q3. Credit Rating?When consumcers apply for credit, their credit is rated using FICO scores. Credit ratings are given below for a sample of applicants for car loans.
661 595 548 730 791 678 672 491 492 583 762 624 769 729 734 706 Using the sample data to construct a 99% confidence interval for the mean FICO score of all applicants for credit
If one bank requires a credit rating of at least 620 for a car loan, does it appear that almost all applicants will have suitable credit ratings?
Q4. Stimulated Data?Randomly generate 500 IQ scores from a population having a normal distribution, a mean of 100, and a standard deviation of 15. Record the sample statistics here.
Confidence intervals are typically constructed with confidence levels around 90%, 95%, or 99%. Instead of constructing such a typical confidence interval, use the generated values to construct a 50% confidence interval.
Does the above confidence interval have limits that actually do contain the true population mean, which we know is 100?
Repeat the above procedure 9 more times and list the resulting 50% confidence intervals
Among the total of the confidence intervals constructed, how many of them actually do contain the true population mean of 100? Is this result consistent with the fact that the level of confidence used is 50%?
Quality Control of Doughnuts?The Hudson Valley Bakery makes doughnuts that are packaged in boxes with labels stating that there are 12 doughnuts weighing a total of 42 oz. If the variation among the doughnuts is too large, some boxes will be underweight (cheating consumers) and others will be overweight (lowering profit). A consumer would not be happy with a doughnut so small that it can be seen only with an electron microscope, nor would a consumer be happy with a doughnut so large that it resembles a tractor tire. The quality control supervisor has found that he can stay out of trouble if the doughnuts have a mean of 3.50 oz and a standard deviation of 0.06 oz or less. Twelve doughnuts are randomly selected form the production line and weighted, with the results given in ounces.
3.43 3.37 3.58 3.50 3.68 3.61 3.42 3.52 3.66 3.50 3.36 3.42
Construct a 95% confidence interval for σ, then determine whether the quality control supervisor is in trouble.