91影视

Given in the question that, We need to check whether the conditions for performing the chi-square test are met in exercises 28 and 30 .

Given:

For both questions, use the provided observation table.

The Expected table is,

The chi-suare test must meet the following requirements:

• There are two category variables.
• There are two or more categories for each variable.
• Independent observation
• The anticipated frequency is at least 1 or at least 5 for the vast majority of cells (80%).

Because the information provided meets all of the criteria. As a result, the chi-square test can be used on the data set in question.

Given in the question that, We need to use Table C to find the $P$-value. Then use our calculator's ${蠂}^2\mathrm{cdf}$command.

The test statistics for exercise 30 are $22.4260$, respectively.

$df=(n-1)(m-1)$

$p-$value $=P\left({蠂}^2>{蠂}_{\text{test}}^2\right)$

For both test values, the degree of freedom can be determined as follows:

$df=(5-1)(3-1)$

$=8$

To find $p$-value on TI83, use the following command: $"{蠂}^{2}cdf(22.4260,99,8)"$

The result is,

Given in the question that, We need to interpret the $P$-value from the calculator in context.

The null and alternative hypothesis are numbered 30

$H_0:\left(\begin{array}{l}\text{There is no difference between Black,}\\ \text{Hispanic, and White parents}\end{array}\right)$

width="313" height="48" role="math">H1:There is a difference between Black,Hispanic, and White parents

The p-value shows the possibility of generating results as extreme as the test statistic value if the null hypothesis is true.

The probability of obtaining a sample as extreme as or more extreme than the current sample is $0.0042$if there is no link between black, Hispanic, and white parents.

Given in the question that, we need to justify our conclusion

When the p-value is less than the level of significance, the null hypothesis is rejected.

The p-value is smaller than the level of significance in this case. As a result, the null hypothesis is ruled out.

As a result, there is enough data to establish that black, Hispanic, and white parents have different parenting styles.