According to the Carnegie unit system, the recommended number of hours students should study per unit is 2. Are statistics students' study hours different from the recommended number of hours per unit? The data show the results of a survey of 16 statistics students who were asked how many hours per unit they studied. Assume a normal distribution for the population. 1.5, 2, 2.9, 3.8, 4.6, 1.1, 1.8, 2.6, 1.4, 2.8, 4.5, 1.2, 1, 0.7, 3, 1.2 What can be concluded at the αα = 0.05 level of significance? For this study, we should use Select an answer t-test for a population mean z-test for a population proportion The null and alternative hypotheses would be: H0:H0: ? μ p Select an answer < ≠ = > H1:H1: ? p μ Select an answer < ≠ = > The test statistic ? z t = (please show your answer to 3 decimal places.) The p-value = (Please show your answer to 4 decimal places.) The p-value is ? > ≤ αα Based on this, we should Select an answer reject fail to reject accept the null hypothesis. Thus, the final conclusion is that ... The data suggest that the population mean study time per unit for statistics students is not significantly different from 2 at αα = 0.05, so there is insufficient evidence to conclude that the population mean study time per unit for statistics students is different from 2. The data suggest the populaton mean is significantly different from 2 at αα = 0.05, so there is sufficient evidence to conclude that the population mean study time per unit for statistics students is different from 2. The data suggest the population mean is not significantly different from 2 at αα = 0.05, so there is sufficient evidence to conclude that the population mean study time per unit for statistics students is equal to 2.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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According to the Carnegie unit system, the recommended number of hours students should study per unit is 2. Are statistics students' study hours different from the recommended number of hours per unit? The data show the results of a survey of 16 statistics students who were asked how many hours per unit they studied. Assume a normal distribution for the population.

1.5, 2, 2.9, 3.8, 4.6, 1.1, 1.8, 2.6, 1.4, 2.8, 4.5, 1.2, 1, 0.7, 3, 1.2

What can be concluded at the αα = 0.05 level of significance?

For this study, we should use Select an answer t-test for a population mean z-test for a population proportion
The null and alternative hypotheses would be:

H0:H0: ? μ p Select an answer < ≠ = >

H1:H1: ? p μ Select an answer < ≠ = >

The test statistic ? z t = (please show your answer to 3 decimal places.)
The p-value = (Please show your answer to 4 decimal places.)
The p-value is ? > ≤ αα
Based on this, we should Select an answer reject fail to reject accept the null hypothesis.
Thus, the final conclusion is that ...
- The data suggest that the population mean study time per unit for statistics students is not significantly different from 2 at αα = 0.05, so there is insufficient evidence to conclude that the population mean study time per unit for statistics students is different from 2.
- The data suggest the populaton mean is significantly different from 2 at αα = 0.05, so there is sufficient evidence to conclude that the population mean study time per unit for statistics students is different from 2.
- The data suggest the population mean is not significantly different from 2 at αα = 0.05, so there is sufficient evidence to conclude that the population mean study time per unit for statistics students is equal to 2.
Interpret the p-value in the context of the study.
- If the population mean study time per unit for statistics students is 2 and if you survey another 16 statistics students, then there would be a 42.50732002% chance that the sample mean for these 16 statistics students would either be less than 1.74 or greater than 2.
- There is a 42.50732002% chance that the population mean study time per unit for statistics students is not equal to 2.
- There is a 42.50732002% chance of a Type I error.
- If the population mean study time per unit for statistics students is 2 and if you survey another 16 statistics students then there would be a 42.50732002% chance that the population mean would either be less than 1.74 or greater than 2.
Interpret the level of significance in the context of the study.
- There is a 5% chance that the population mean study time per unit for statistics students is different from 2.
- There is a 5% chance that students just don't study at all so there is no point to this survey.
- If the population mean study time per unit for statistics students is 2 and if you survey another 16 statistics students, then there would be a 5% chance that we would end up falsely concuding that the population mean study time per unit for statistics students is different from 2.
- If the population mean study time per unit for statistics students is different from 2 and if you survey another 16 statistics students, then there would be a 5% chance that we would end up falsely concuding that the population mean study time per unit for statistics students is equal to 2.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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