Researchers examine the relationship between mother's education level and hours spent on homework each week for a random sample of 80 high school students. Students were grouped into four categories based on their mother's education level. Below are the summary statistics and graphs for the samples. Use this information to answer the next three questions.Responses: HomeWorkFactors: MotherEdConsolidated Response statistics by factor MotherEdConsolidated n Mean Std. Dev. Std. Error AA, trade, or some college 24 8.5 5.9 1.2 BA or above 35 8.5 6.0 1.0 HS grad 19 7.9 5.4 1.2 no HS diploma 4 4.3 1.5 0.8 Which are appropriate ways to state the alternative hypothesis? Check all that apply. Group of answer choices There is a no relationship between mother's education level and the hours high school students devote to homework each week. There is a relationship between mother's education level and the hours high school students devote to homework each week. µ1 ≠ µ2 ≠ µ3 ≠ µ4, where µ1 is the mean homework hours per week for the population of high school students whose mothers' highest education level is AA, trade, or some college. µ2 is the mean homework hours per week for the population of high school students whose mothers' highest education level is BA or above. µ3 is the mean homework hours per week for the population of high school students whose mothers' highest education level is HS grad. µ4 is the mean homework hours per week for the population of high school students whose mothers' highest education level is no HS diploma. The mean homework hours per week differ for the four populations of high school students defined by their mothers' highest education level (AA/trade/some college, BA or above, HS grad, no HS diploma.)
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
Researchers examine the relationship between mother's education level and hours spent on homework each week for a random sample of 80 high school students. Students were grouped into four categories based on their mother's education level. Below are the summary statistics and graphs for the samples.
Use this information to answer the next three questions.
Responses: HomeWork
Factors: MotherEdConsolidated
Response statistics by factor
| MotherEdConsolidated | n | Mean | Std. Dev. | Std. Error |
|---|---|---|---|---|
| AA, trade, or some college | 24 | 8.5 | 5.9 | 1.2 |
| BA or above | 35 | 8.5 | 6.0 | 1.0 |
| HS grad | 19 | 7.9 | 5.4 | 1.2 |
| no HS diploma | 4 | 4.3 | 1.5 | 0.8 |
µ1 ≠ µ2 ≠ µ3 ≠ µ4, where
µ1 is the mean homework hours per week for the population of high school students whose mothers' highest education level is AA, trade, or some college.
µ2 is the mean homework hours per week for the population of high school students whose mothers' highest education level is BA or above.
µ3 is the mean homework hours per week for the population of high school students whose mothers' highest education level is HS grad.
µ4 is the mean homework hours per week for the population of high school students whose mothers' highest education level is no HS diploma.
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