Question

Two students are interested in whether or not there is variation in their test scores for math class. There are 15 total math tests they have taken so far. The first student's grades have a standard deviation of 38.2. The second student's grades have a standard deviation of 22.5. The second student thinks his scores are lower. State the null and alternative hypotheses.

Answer 1

The null hypothesis is that there is no variation in the test scores between the two students, while the alternative hypothesis is that there is variation. The F statistic is used to compare the variation between and within groups, and the p-value represents the probability of obtaining the observed data assuming the null hypothesis is true. At a 5 percent significance level, we reject the null hypothesis if the p-value is less than 0.05.

Step-by-step explanation:

52. Null hypothesis: There is no variation in the test scores between the two students. Alternative hypothesis: There is variation in the test scores between the two students.

53. The F statistic: The F statistic is a value calculated in an analysis of variance (ANOVA) test that compares the variation between groups to the variation within groups.

54. The p-value: The p-value is the probability of obtaining the observed data, or more extreme data, assuming that the null hypothesis is true.

55. At the 5 percent significance level, do we reject the null hypothesis?: To determine if we reject the null hypothesis, we compare the p-value to the significance level. If the p-value is less than the significance level (0.05), we reject the null hypothesis.

Answer 2

`H_0=\sigma_1 =\sigma_2`

`H_a=\sigma_1 >\sigma_2`

Step-by-step explanation:

From the question we are told that

Number of math tests n=15

standard deviation 1
`\sigma _1=38.2`

standard deviation 1
`\sigma _2=22.5`

Generally given the two tailed test the null hypothesis is given as

`H_0=\sigma_1 =\sigma_2`

Generally given the two tailed test the null hypothesis is given as

`H_a=\sigma_1 >\sigma_2`