Discuss the below:
Q1. Although many people think they can put a meal on the table in a short period of time, an article reported that they end up spending about 40 minutes doing so. Suppose another study is conducted to test the validity of this statement. A sample of 25 people is selected, and the length of time to prepare and cook dinner (in minutes) is recorded, with the following results
a) Is there evidence that the population mean time to prepare and cook dinner is different from 40 minutes? Use the p-value approach and a level of significance of 0.05.
b) What assumption about the population distribution is needed in order to conduct the t test in (a)?
| Time |
| 44.0 |
| 51.9 |
| 49.7 |
| 40.0 |
| 55.5 |
| 33.0 |
| 43.4 |
| 41.3 |
| 45.2 |
| 40.7 |
| 41.1 |
| 49.1 |
| 30.9 |
| 45.2 |
| 55.3 |
| 52.1 |
| 55.1 |
| 38.8 |
| 43.1 |
| 39.2 |
| 58.6 |
| 49.8 |
| 43.2 |
| 47.9 |
| 46.6 |
Q2. Nondestructive evaluation is a method that is used to describe the properties of components or materials without causing any permanent physical change to the units. It includes the determination of properties of materials and the classification of flaws by size, shape, type, and location. This method is most effective for detecting surface flaws and characterizing surface properties of electrically conductive materials. Data were collected that classified each component as having a flaw or not, based on manual inspection and operator judgement, and the data also reported the size of the crack in the material. Do the components classified as unflawed have a smaller mean crack size than components classified as flawed? The results in terms of crack size (in inches)
a.) Assuming that the population variances are equal, is there evidence that the mean crack size is smaller for the flawed specimens than for the flawed specimens?
| Type |
Crack size |
| 0 |
0.003 |
| 0 |
0.004 |
| 0 |
0.012 |
| 0 |
0.014 |
| 0 |
0.021 |
| 0 |
0.023 |
| 0 |
0.024 |
| 0 |
0.030 |
| 0 |
0.034 |
| 0 |
0.041 |
| 0 |
0.041 |
| 0 |
0.042 |
| 0 |
0.043 |
| 0 |
0.045 |
| 0 |
0.057 |
| 0 |
0.063 |
| 0 |
0.074 |
| 0 |
0.076 |
| 1 |
0.022 |
| 1 |
0.026 |
| 1 |
0.026 |
| 1 |
0.030 |
| 1 |
0.031 |
| 1 |
0.034 |
| 1 |
0.042 |
| 1 |
0.043 |
| 1 |
0.044 |
| 1 |
0.046 |
| 1 |
0.046 |
| 1 |
0.052 |
| 1 |
0.055 |
| 1 |
0.058 |
| 1 |
0.060 |
| 1 |
0.060 |
| 1 |
0.070 |
| 1 |
0.071 |
| 1 |
0.073 |
| 1 |
0.073 |
| 1 |
0.078 |
| 1 |
0.079 |
| 1 |
0.079 |
| 1 |
0.083 |
| 1 |
0.090 |
| 1 |
0.095 |
| 1 |
0.095 |
| 1 |
0.096 |
| 1 |
0.100 |
| 1 |
0.102 |
| 1 |
0.103 |
| 1 |
0.105 |
| 1 |
0.114 |
| 1 |
0.119 |
| 1 |
0.120 |
| 1 |
0.130 |
| 1 |
0.160 |
| 1 |
0.306 |
| 1 |
0.328 |
| 1 |
0.440 |