me solve this subject: stats and prob 1.) Hypothesis Testing Proportions Over the past few decades, public health officials have examined the link between weight concerns and teen girls' smoking. Researchers surveyed a group of 273 randomly selected teen girls living in Massachusetts (between 12 and 15 years old). After four years the girls were surveyed again. 63 said they smoked to stay thin. Is there good enough evidence that more than 30% of the teen girls smoke to stay thin? The alternative hypothesis is: H a : p < 0.30 H a : p < 0.30 H a : p 0.30 H a : p 0.30 H a : p 0.30 H a : p 0.30 H a : p > 0.30 H a : p > 0.30 2.) The blue catfish (Ictalurus Furcatus) is the largest species of North Amercian catfish. The current world record stands at 143 pounds, which was caught in the John H. Kerr Reservoir (Bugg's Island Lake) located in Virginia. According to Amercian Expedition, the average weight of a blue catfish is between 20 to 40 pounds. Given that the largest blue catfish ever caught was at the John H. Kerr Reservoir, you believe that the mean weight of the fish in this reservoir is greater than 40 pounds. a) If you going to test this claim at the 0.05 significance level, what would be your null and alternative hypotheses? H 0 H 0 : H 1 H 1 : b) What type of hypothesis test should you conduct (left-, right-, or two-tailed)? left-tailed right-tailed two-tailed 3.) H 0 : = 48.1 H 0 : = 48.1 H 1 : < 48.1 H 1 : < 48.1 Your sample consists of 20 subjects, with a mean of 47.2 and standard deviation of 3.87. Calculate the test statistic, rounded to 2 decimal places. t = t = 4.) Testing: H 0 : = 58.545 H 0 : = 58.545 H 1 : > 58.545 H 1 : > 58.545 Your sample consists of 31 subjects, with a mean of 59.7. You were given a population standard deviation of 2.51. Calculate the test statistic, rounded to 2 decimal places. z = z = 5.) Testing: H 0 : = 59 H 0 : = 59 H 1 : < 59 H 1 : < 59 Your sample consists of 46 subjects, with a mean of 58.6 and a sample standard deviation (s) of 1.36. Calculate the test statistic, rounded to 2 decimal places. t = t = 6.) Eyeglassomatic manufactures eyeglasses for different retailers. They test to see how many defective lenses they made in a given time period and found that 11% of all lenses had defects of some type. Looking at the type of defects, they found in a three-month time period that out of 34,912 defective lenses, 5830 were due to scratches. Are there more defects from scratches than from all other causes? State the Type I and Type II errors in this case. State the Type I error. Concluding that the proportion of defects from scratches is less than 11%, when the proportion is actually 11%. Concluding that the proportion of defects from scratches is higher than 11%, when the proportion is actually 11%. Concluding that the proportion of defects from scratches is 11%, when in reality it is higher than 11%. Concluding that the proportion of defects from scratches is 11%, when in reality it is less than 11%. State the Type II error. Concluding that the proportion of defects from scratches is higher than 11%, when the proportion is actually 11%. Concluding that the proportion of defects from scratches is less than 11%, when the proportion is actually 11%. Concluding that the proportion of defects from scratches is 11%, when in reality it is less than 11%. Concluding that the proportion of defects from scratches is 11%, when in reality it is higher than 11%. 7.) Your sample consists of 31 subjects, with a mean of 50.2 and standard deviation of 4.83. The population mean is = 48.485 = 48.485 . Calculate the test statistic, rounded to 3 decimal places. t = t = 8.) Your sample consists of 31 subjects, with a mean of 50.2 and standard deviation of 4.83. The population mean is = 48.485 = 48.485 . Calculate the test statistic, rounded to 3 decimal places. t= 9.) For each research question below, select the most appropriate type of statistical test or analysis. In each case, you many assume that all necessary assumptions are met. SCENARIO 1: Does drinking an acoholic beverage reduce stress? A sample of 70 participants were asked to rate their level of stress on a scale of 0 and 100 before drinking an acoholic beverage and then again after drinking an acoholic beverage, and the responses recorded. One-sample test for a mean One-sample test for a proportion Two Independent Samples test for a difference of population means Two Dependent Samples test for mean difference (paired data) Chebyshev Procedure Correlation and regression analysis SCENARIO 2: An English professor wants to determine whether there is a relationship between the amount of time students spend writing a paper and the student's grade on the paper. For a sample of 57 students, the amount of time students spend writing a paper and the student's grade on the paper is recorded. One-sample test for a mean One-sample test for a proportion Two Independent Samples test for a difference of population means Two Dependent Samples test for mean difference (paired data) Chebyshev Procedure Correlation and regression analysis