$\left(\frac{3}{7}x+9\right)-\left(\frac{2}{7}x-3\right)\\\\=\frac{3}{7}x+9-\frac{2}{7}x-(-3)\\\\=\frac{3}{7}x+9-\frac{2}{7}x+3\\\\=(\frac{3}{7}x-\frac{2}{7}x)+(9+3)\\\\=\frac{3-2}{7}x+12\\\\=\boxed{\frac{1}{7}x+12}$

4 0

4 years ago

A researcher claims that the variation in the salaries of elementary school teachers is greater than the variation in the salari

guajiro [1.7K]

Answer:

The null hypothesis is $H_o : \sigma^2_1 = \sigma^2 _2$

The alternative hypothesis is $H_a : \sigma_1 ^2 > \sigma^2_2$

$F_{critical} = 1.8608$

$F = 2.9085$

The decision rule is

Reject the null hypothesis

There is sufficient evidence to support the researchers claim

Step-by-step explanation:

From the question we are told that

The first sample size is $n_1 = 30$

The sample variance for elementary school is $s^2_1 = 8324$

The second sample size is $n_2 = 30$

The sample variance for the secondary school is $s^2_2 = 2862$

The significance level is $\alpha = 0.05$

The null hypothesis is $H_o : \sigma^2_1 = \sigma^2 _2$

The alternative hypothesis is $H_a : \sigma_1 ^2 > \sigma^2_2$

Generally from the F statistics table the critical value of $\alpha = 0.05$ at first and second degree of freedom $df_1 = n_1 - 1 = 30 - 1 = 29$ and $df_2 = n_2 - 1 = 30 - 1 = 29$ is