Question

A university is conducting a survey to study the number of hours students sleep at night during exam week. A sample of 20 students was drawn, and these responses were obtained: 6.5, 5, 8, 5.5, 7, 4, 4.5, 5, 6, 5.5, 4, 7.5, 6, 7, 8, 5, 6, 6.5, 6.5, 5. The standard deviation of the population mean is 2 hours. Arrange the steps in the correct sequence to find the range in which 95% of the sample mean occurs. Tiles The standard error of the mean of the sample is . The range in which 95% of the sample mean occurs is . The range in which 95% of the sample mean occurs is 5.93 + 2 × 0.45 = 6.83 hours and 5.93 − 2 × 0.45 = 5.03 hours. The sample mean is . The 20 students' total number of study hours is 118.5 hours. Calculate the standard deviation.

Answer 1

1. To calculate the mean, we first total the number of hours: The 20 students' total number of study hours is 118.5 hours.
2. We divide by the number of samples to find the mean: The sample mean is 5.93.
3. Next, we find the SD: Calculate the standard deviation.
4. Then we divide SD by the number of samples to get the standard error: the standard error of the mean of the sample is 0.45.
5. Since for a 95% CI, the corresponding z-score is 1.96 ~ 2, we use the formula for CI: mean +/- z*SE, which is: The range in which 95% of the sample mean occurs is 5.93 + 2 × 0.45 = 6.83 hours and 5.93 − 2 × 0.45 = 5.03 hours.
6. Finally: The range in which 95% of the sample mean occurs is (5.03, 6.83).