ACTIVITY SET 13 March 24 Stat 200 Sections 4-6Activity 13. 1 a. An instructor asked students to randomly choose one of the numbers 1, 2, 3,4, 5, 6, 7. With random picking, the chance of picking the number "1" is 1/7. The instructor believes that students will pick the number "3" more often than would occur by random picking. In words, what are null and alternative hypotheses for the instructor?Null hypothesis:Alternative hypothesis:Express the hypotheses in statistical notation. H0: Ha: 12b. The maker of M&Ms candy claims that 10% of all M&Ms are red. Ralph thinks otherwise – he believes the percent is less than 10%. In words, what are null and alternative hypotheses for Ralph?Null hypothesis:Alternative hypothesis:Express the hypotheses in statistical notation. H0: Ha: Next week we’ll focus on testing hypotheses about means. Here are symbols for either one mean or the difference between two means (like difference between mean GPAs of men and women).Parameter of interest SymbolOne mean Difference between means of two independent groups1 2c. A medical researcher wants to demonstrate that the mean body temperature for healthy people is in fact less than the commonly accepted value of 98.6 Fahrenheit. In words, what are null and alternative hypotheses for the researcher?Null hypothesis:Alternative hypothesis:Express the hypotheses in statistical notation. H0: Ha: d. We want to show that the mean scores on a memory test will be different for women (group 1) and men(group 2). In words, what are null and alternative hypotheses in this situation.Null hypothesis:Alternative hypothesis:Express the hypotheses in statistical notation. H0: Ha: Activity 13.2 DEFINITIONS A type 1 error occurs if we incorrectly pick the alternative hypothesis (pick it when null is really the truth) A type 2 error occurs if we incorrectly pick the null hypothesis (pick it when the alternative is really the truth). a. Refer back to parts b (about M&Ms) of Activity 13.1. Explain what the type 1 and type 2 errors are in this situation. Do this in terms of the "real world" situation. b Refer back to parts d (about memory of men and women) of Activity 13.1. Explain what the type 1 and type 2 errors are in this situation. Do this in terms of the "real world" situation.Activity 13.3When testing hypotheses about a proportion the test statistic is npppp)1(ˆ000. This measures the difference between the sample p and the null hypothesis value p0. The bottom of the test statistic is a standard error computed using the null hypothesis value. In each case, calculate the value of the test statistic z, and show work.a. In a clinical trial of a treatment for a psychiatric problem, the proportion of successful treatments is .72, with n = 200 patients participating. Hypotheses are: null: p = .65 and alternative: p > .65.b. In a sample of n = 400 M&Ms, there are 28 red candies. Hypotheses are: null: p = .10 and alternative: p < .10, with p = population proportion that is red. c. In a taste test, 63 of 100 tasters prefer Cola A over Cola B. We’re testing null: p = .50 versus alternative: p ≠ .50, where p = population proportion that prefers Cola A.d. In a poll, 80 of 160 U.S. adults say they approve of the president’s job performance. We’re testing null: p = .50 versus alternative: p ≠ .50, where p = population proportion approving of thepresident.Activity 13.4 When testing hypotheses about a population proportion, the rules for using the normal curve to find a p-value are:Symbol in Ha What to do:< (less than) Find the probability less than z> (greater than) Find the probability greater than z  (not equal) Find the probability less than the negative version of z, then multiply by 2.Use either Table A.1 in the book or Minitab’s Calc>Probability Distributions>Normal to help you find p-values for each of the situations in Activity 13.3.a. Find p-value for part a of activity 13.3and draw a sketch showing the region. b. Find p-value for part b of activity 13.3 and draw a sketch showing the region.c. Find p-value for part c of activity 13.3 and draw a sketch showing the region.d. Find p-value for part d of activity 13.3 and draw a sketch showing the region.Activity 13.5 Refer to activities 13.3 and 13.4. For each part, indicate whether the null or the alternative should be picked.a. b.c.