This is a group Project: Please focus on the results submitted by GROUP MEMBER: YEWANDE ADENIYI It is my results that you will use in conducting the other test analysis for the problem state below: Problem: Conduct a hypothesis test analysis to determine if there is a statistical difference between the ages of the sexes in the group. State what you are testing. Write the hypotheses. Show the relevant numbers. Then explain your results. Use alpha = .05. 2) This week you will analyze if women drink more sodas than men. For the purposes of this DQ, assume that in the past there has been no difference. However, you have seen lots of women drinking sodas the past few months. You will perform a hypothesis test to determine if women now drink more sodas than men. State what you are testing. Write the hypotheses. Show the relevant numbers. Then explain your results. Use alpha = .05.1) A bowler who has averaged 196 pins in the past year is asked to experiment with a ball made of a new kind of material. He rolls several games with the new ball. Has the new ball improved his game? Null Hypothesis: Ho: µ = 196 Alternative Hypothesis: H1: µ > 196 2) An advertisement claims that chewing NoCav gum reduces cavities. To test the claim, you conduct a study in which participants who chew the gum are compared to the national average of 3 cavities found per year. Null Hypothesis: Ho: µ = 3 Alternative Hypothesis: H1: µ < 3 3) In a speech to the Chamber of Commerce, a city councilman claims that in his city less than 15% of the adult male population are unemployed. An opponent in the upcoming election wants to test the councilman’s claim. Null hypothesis: Ho : p = 0.15 Alternative hypothesis: Ha : p < 0.15 4) The councilman is starting to get worried about the upcoming election. He has enjoyed 63% support for several years, but the political climate has been changing. He wants to know if his support has changed. Null hypothesis: Ho : p = 0.63 Alternative hypothesis: Ha : p ≠ 0.63 5) A production process is considered to be under control if the machine parts it makes have a mean length of 35.50 mm with a standard deviation of 0.45 mm. Whether or not the process is under control is decided each morning by a quality control engineer who bases his decision on a random sample of size 36. Should he ask for an adjustment of the machine on a day when he obtains a mean of 35.62 mm? Ho: µ = 35.50 ± s(.45) Ha: µ ≠ 35.50 ± s(.45) 6) Jim, the owner of Jim’s Grocery, knows that Plain Chips have always outsold Spicy chips. However, sales of Spicy chips have been increasing. Jim wants to determine if the average weekly sales of Spicy chips have indeed surpassed that of Plain chips. Ho: µ(Spicy chips) ≤ µ(Plain chips) Ha: µ(Spicy chips) > µ(Plain chips) 7) Jim now wants to know if Plain and Spicy chips have the same percentage of defective product (i.e. underfilled bags, torn bags, wrong flavor in the bags, etc.). Null Hypothesis: Plain Chip product defects ≠ Spicy Chip product defects. Alternate Hypothesis: Plain Chip product defects = Spicy Chip product defects 8) The Great Vehicle Co. just introduced New SUV, claiming it can pull more weight than Old SUV. After testing 150 vehicles of each model, Old SUV had a mean pull weight of 5032 pounds with a standard deviation of 72 pounds. New SUV had a mean pull weight of 5462 pounds with a standard deviation of 154 pounds. Is the claim valid at a .05 level of significance? Ho : New SUV can pull 5032 lbs ± 72 lbs Ha: New SUV can pull more than 5032 lbs ± 72 lbs 9) The Great Vehicle Co. has a competitor, Amazing Autos, that claims people who purchase its competing vehicle, the Sport Off Road Vehicle (SORV), have higher customer satisfaction than New SUV. Out of 736 people who purchased the SORV last month, 534 said they were satisfied. Out of 521 people who purchased New SUV last month, 375 said they were satisfied. Is there a higher percentage of people who are satisfied with the SORV than with New SUV? Null Hypothesis: Customer satisfaction with SORV = Customer satisfaction with New SUV Ho: SORV = New SUV Alternate Hypothesis: SORV satisfaction > New SUV satisfaction. Ha: SORV > New SUV 10) The Great Vehicle Company wants to counter Amazing Autos’s claim by making its own claim that New SUV has a lower percentage of defective vehicles. The research team tested 536 vehicles of each model and found that SORV had 53 defective units, while New SUV had only 51 defective units. Null Hypothesis: The New SUV percentage of defects = SORV percentage of defects Ho: New SUV = SORV Alternate Hypothesis: The New SUV percentage of defects < SORV percentage of defects Ha: New SUV < SORV Top of Form Statistics Questions Group Member- Yewande AdeniyiTotal views: 12 (Your views: 5) Respondent Age Num. Vitamins /day Num. Carb. Sodas /day Num. Alc. Bev. /month Been to Disneyland 1 22 1 0 1 Y 2 24 3 2 3 Y 3 45 2 4 5 Y 4 19 2 3 3 N 5 33 3 1 2 Y 6 27 0 0 6 N 7 21 4 5 2 Y 8 25 2 3 5 Y 9 30 1 2 2 Y 10 50 2 4 4 N Yewande Adeniyi From the data set, the sample statistics are: Sample mean: x = 2 Sample standard deviation: s = 1.1547 Sample size: n = 10 The hypotheses are: Null hypothesis: Ho : µ = 3 Alternative hypothesis: Ha : µ ≠ 3 Because of the small sample size, and the unknown population variance/standard deviation, the t-statistic must be used for this test. With a sample size of 10, there are 10 – 1 = 9 degrees of freedom. The critical values for a two-tailed test with α = 0.05 with 9 degrees of freedom are tc = -2.262 and tc = 2.262. The test statistic is: t test = x - µ = 2 - 3 = -2. 7386 s / √n 1.1547/ √10 Since the test statistic value of -2.7386 is less than the critical value of -2.262, the decision is to reject the null hypothesis. There is sufficient evidence at the 0.05 level of significance to support a claim that the mean number of vitamins taken per day is different than 3. 2) Use your data from above. Analyze if more than 58% support an issue or partake in an activity. (Question E above). Write the hypotheses. Show the relevant numbers. Then explain your results. Use alpha = 0.05. The number of respondents that reported having been to Disneyland was 7, out of a total of ten survey participants. (See data on last page.) The sample proportion is then: p = 7 = 0.70 10 The hypotheses are: Null hypothesis: Ho : p = 0.58 Alternative hypothesis: Ha : p > 0.58 For a right-tailed test of a proportion, with α = 0.05, the critical value is z = 1.645. The test statistic is: Z test = p - p = 0.70 - 0.58 = 0.7689 √p ( 1 - p ) / n √(0.58) (1 - 0.58) / 10 Since the test statistic of 0.7689 is less than the critical value of 1.645, the decision is to fail to reject the null hypothesis. The conclusion is that there is insufficient evidence at the 0.05 level of significance to support a claim that more than 58% have been to Disneyland Group Member: Alberto Posada Gender Age Vitamins per Day Carbonated Soda Drinks per Day Alcoholic Beverages per Month Do you like Obama Male 22 1 0 12 No Male 25 15 0 30 No Male 29 0 2 14 Yes Male 33 3 1 5