Question: The project consists of four questions involving hypothesis tests. For each problem, do the following: Identify the type of test. (z-test, t-test, matched pairs test, Chi-squared test of good fit or Chi-squared test of independence) State why you chose that particular test and the condition(s) required for conducting that test. Write Ho and Ha both mathematically and in context. Calculate the test statistic (z, t or X^2). Show the correct formula for the calculation even if you get the number from your calculator. Find the p-value for the test. (Use your calculator!) Make a decision about the null hypothesis (Reject Ho or Do Not Reject Ho) Make a conclusion based on your decision (Write a sentence to answer the question asked). Please show me how you got the answers. Problem 1 The recommended daily allowance (RDA) of calcium for women between the ages of 18-25 is 1200 milligrams. Researchers who were involved in a large-scale study of women’s bone issues suspected that the participants had lower calcium intakes that were recommended. They measured the calcium intake for 20 women between the ages of 18 and 25. The number milligrams consumed by each of the 20 women is listed below. Do these data give convincing evidence that the researcher’s suspicion is correct? 1205 1198 1182 1193 1187 1197 1215 1191 1189 1179 1193 1188 1194 1207 1193 1210 1185 1194 1196 1190 Problem 2 The average height of adult men is 5’10” with a known standard deviation, σ, of 2.5″. After measuring all the male seniors for caps and gowns, a PTSA member stated “this year’s senior class at seems to be taller than normal”. To investigate her theory the PTSA computed the average height of 40 of the males in the senior class and found they had a mean height of 71″. Does the data provide convincing evidence that the PTSA member’s conclusion was correct? (Use α = .05) Problem 3 The Federal Drug Administration (FDA) requires warning label on medication that may slow reaction times for those people taking the medication. A pharmaceutical company is planning to submit a new drug for FDA approval, so it conduct a test to determine if the drug slow the reaction times of people taking the medication. Fifteen people are tested before and after taking the drug and their reactions times (in seconds) on a standard skill tests are measured. The results of the test are shown in the table below. Does the data indicate the need for a warning label on the drug? (Use α = .05) Person Before After 1 1.42 1.48 2 1.87 1.75 3 1.34 1.31 4 0.98 1.22 5 1.51 1.58 6 1.43 1.57 7 1.52 1.48 8 1.61 1.55 9 1.37 1.54 10 1.49 1.37 11 0.95 1.07 12 1.32 1.35 13 1.68 1.77 14 1.44 1.44 15 1.17 1.27 Problem 4 The manufacturer of Lucky Charms breakfast cereal, General Mills, claims that all marshmallow shapes are equally represented in each box of cereal. Susie, a 4 year old who really likes rainbows, refuses to eat breakfast one morning because there were not enough rainbows in her bowl of cereal. Susie’s mom wonders if shape distribution in the box of cereal is “unfair” to rainbows. She pours out the remaining cereal and separates it by shape. The results are shown in the table below. Is there enough evidence at the α = .05 level to disprove the manufacture’s claim of equal distribution of shapes? Shape Hearts Stars Horseshoes Clovers Blue Moons Rainbows Hourglasses Count 47 53 42 60 57 40 51 =