Use the following listed chest deceleration measurements (in g, where g is the force of gravity) from samples of small, midsize and large cars. Assume that we plan to use a 0.05 significance level to test the claim that the different size categories have the same mean chest deceleration in the standard crash test. Small Midsize Large 44 36 32 39 53 45 37 43 41 54 42 38 39 52 37 44 49 42
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Use the following listed chest deceleration measurements (in g, where g is the force of gravity) from samples of small, midsize and large cars. Assume that we plan to use a 0.05 significance level to test the claim that the different size categories have the same
Small |
Midsize |
Large |
44 |
36 |
32 |
39 |
53 |
45 |
37 |
43 |
41 |
54 |
42 |
38 |
39 |
52 |
37 |
44 |
49 |
|
42 |
|
|
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- "Durable press" cotton fabrics are treated to improve their recovery from wrinkles after washing. "Wrinkle recovery angle" measures how well a fabric recovers from wrinkles. Higher is better. Here are data on the wrinkle recovery angle (in degrees) for two types of treated fabrics: Permafresh 15 12 16 13 11 14 10 Hylite 16 20 18 15 19 A manufacturer wants to know how large is the difference in mean wrinkle recovery angle. Give a 90% confidence interval for the difference in mean wrinkle recovery angle: [three decimal accuracy] [three decimal accuracy]The average farm size in Micah's country is 445 acres. The average farm size in Johanna's country is 485 acres. (a) Determine whether the following statement is true or false. If you wanted to determine if there is a statistically significant difference between the two countries, the parameter of interest would be uM - H7, where HM = mean size of all farms in Micah's country u, = mean size of all farms in Johanna's country. O True O False (b) If you wanted to determine if there is a statistically significant difference between the two countries, what would be your null hypothesis? O Ho: H, = 445 Ho: HM - Hy > o O Ho: HM - H, = 0 O Ho: HM = 485 (c) What would be your alternative hypothesis? O H: HM - H3 0 O H: HM - H, + 0 O H2: HM+ 485A pharmaceutical manufacturer forms tablets by compressing a granular material that contains the active ingredient and various fillers. The force in kilograms (kg) applied to the tablet varies a bit and follows the Normal distribution with mean 11.5 kg and standarddeviation 0.2 kg. The process specifications call for applying a force between 11.2 and 12.2 kg. i. What percent of tablets are subject to a force that meets the specifications?ii. The manufacturer adjusts the process so that the mean force is at the center of the specifications, μ = 11.7 kg. The standard deviation remains 0.2 kg. What percent now meets the specifications? iii. Calculate the 25th percentile (P25) and the 75th percentile (P75) of the distribution.
- A quality control engineer needs to ensure that the caps on shampoo bottles are fastened correctly. If the caps are fastened too loosely, they may fall off during shipping. The target torque value for fastening the caps is 18. The engineer collects a random sample of 68 bottles and tests the amount of torque that is needed to remove the caps. Histogram of Torque 14 12 10 12 16 20 24 28 Torque 1. What are the cases in this study? [Select] [ Select ] 2. The shape of the data distribution can be best described as 3. Using the the histogram, the exact sample mean and median values can be determined [ Select ] 4. Based on the histogram, the 5th percentile of the torque values is likely closest to v ( Select ] cannot beletermined 12 kely interval containing the lower quartile is 15 [Select ] FrequencyA new production process is being contemplated for the manufacture of stainless steel bearings. Measurements of the diameters of random samples of bearings from the old and the new processes produced the following data: Old: 16.3 15.9 15.8 16.2 16.1 16.0 15.7 15.8 15.9 16.1 16.3 16.1 15.8 15.7 15.8 15.7 New: 15.9 16.2 16.0 15.8 16.1 16.1 15.8 16.0 16.2 15.9 15.7 16.2 15.8 15.8 16.2 16.3 Can you conclude at the 5% level that one process yields a different mean size bearing than the other? a. b. Can you conclude at the 5% level that the variance of the new procedure is lower than the older procedure?The degenerative disease osteoarthritis most frequently affects weight-bearing joints such as the knee. Stance duration (ms) was measured in separate samples of younger and older adults. younger: n=22 mean=801 s=117 older: n=16 mean=780 s=81 Test the claim that the true average stance is different between younger and older adults. Let population 1= younger population 2= older a. What is the appropriate procedure to test the claim? b.What is the degrees of freedom? Use the conservative formula. c.At 0.05 significance level, what is/are the critical value/s? d.What is the value of the test statistic? Use 2 decimal places e.Construct a 95% confidence interval estimate, what is the margin of error? Use 2 decimal places.
- Patients with rheumatoid arthritis are at a greater risk of developing osteoporosis. The reasons are not well understood due to the difficulty in qualitatively assessing bone metabolism and mineral content. A researcher measures human calcitonin (HCT) levels in men with rheumatoidarthritis. The researcher randomly selects 43 men with rheumatoid arthritis and measured the mean HCT level of 33.8 pg/mL. Assume that HCT for individuals with rheumatoid arthritis follows a normal distribution with standard deviation σ = 23.6 pg/mL. 3. Create a 95% confidence interval for the population mean HCT.Patients with rheumatoid arthritis are at a greater risk of developing osteoporosis. The reasons are not well understood due to the difficulty in qualitatively assessing bone metabolism and mineral content. A researcher measures human calcitonin (HCT) levels in men with rheumatoidarthritis. The researcher randomly selects 43 men with rheumatoid arthritis and measured the mean HCT level of 33.8 pg/mL. Assume that HCT for individuals with rheumatoid arthritis follows a normal distribution with standard deviation σ = 23.6 pg/mL. 6. Describe the effect on your confidence interval if you increase or decrease the samplesizePatients with rheumatoid arthritis are at a greater risk of developing osteoporosis. The reasons are not well understood due to the difficulty in qualitatively assessing bone metabolism and mineral content. A researcher measures human calcitonin (HCT) levels in men with rheumatoidarthritis. The researcher randomly selects 43 men with rheumatoid arthritis and measured the mean HCT level of 33.8 pg/mL. Assume that HCT for individuals with rheumatoid arthritis follows a normal distribution with standard deviation σ = 23.6 pg/mL. 7. Describe a situation where a researcher would want to use a larger confidence level than 95% and a situation where a smaller confidence level would be preferred.
- Patients with rheumatoid arthritis are at a greater risk of developing osteoporosis. The reasons are not well understood due to the difficulty in qualitatively assessing bone metabolism and mineral content. A researcher measures human calcitonin (HCT) levels in men with rheumatoidarthritis. The researcher randomly selects 43 men with rheumatoid arthritis and measured the mean HCT level of 33.8 pg/mL. Assume that HCT for individuals with rheumatoid arthritis follows a normal distribution with standard deviation σ = 23.6 pg/mL. 4. Explain in detail what the 95% Confidence Interval for the mean HCT represents within this context.The sulphur dioxide concentration (in percent) of gases collected from the eruptions of two volcanoes was measured. At each volcano, thirty measurements were taken. The following is the data set. Question: Accept or reject the null hypothesis that there is no difference in sulphur dioxide content in the composition of gases in two eruptions at the 0.05 level of significance? Draw your normal curve for supportTennis elbow is thought to be aggravated by the impact experienced when hitting the ball. The article Forces on the Hand in the Tennis One-Handed Backhand reported the force (Newtons) on the hand just after impact on a one-handed backhand drive for six advanced players and for eight intermediate players. Type Of player Size Mean SD Advanced 8 45.3 12.1 Intermediate 10 22.4 10.2 1) Calculate a 95% CI for the difference of true average for advanced players (µ1) and the true average for intermediate players (µ2). 2) Does your interval provide good evidence for concluding that the two µs are different? 3) Would you have reached the same conclusion by calculating a CI for µ2 − µ1 (i.e., by reversing the 1 and 2 labels on the two types of players)? Explain
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