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3 years ago

I need help finding the answers

Mathematics

1 answer:

Korolek [52]3 years ago

3 0

1. 74.84
2. 28.1
3. 447.3

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A committee at the College Board has been asked to study the SAT math scores for students in Pennsylvania and Ohio. A sample of

ozzi

Answer:

Step-by-step explanation:

From the given information:

The null hypothesis and the alternative hypothesis can be computed as:

$H_0 :\mu_1 -\mu_2 = 0$ (i.e. there is no difference between the SAT score for students in both locations)

$H_1 :\mu_1 -\mu_2 \geq0$ (i.e. there is a difference between the SAT score for students in both locations)

The test statistics using the students' t-test for the two-samples; we have:

$t = \dfrac{\overline x_1 -\overline x_2}{\sqrt{\dfrac{s_1^2}{n_1}+\dfrac{s_2^2}{n_2} } }$

$t = \dfrac{580 -530}{\sqrt{\dfrac{105^2}{45}+\dfrac{114^2}{38} } }$

$t = \dfrac{50}{\sqrt{\dfrac{11025}{45}+\dfrac{12996}{38} } }$

$t = \dfrac{50}{\sqrt{245+342 } }$

$t = \dfrac{50}{\sqrt{587} }$

$t = \dfrac{50}{24.228}$

t = 2.06

degree of freedom = ( $n_1 + n_2$ ) -2

degree of freedom = (45+38) -2

degree of freedom = 81

Using the level of significance of 0.05

Since the test is two-tailed at the degree of freedom 81 and t = 2.06

The p-value = 0.0426

Decision rule: To reject $H_o$ if the p-value is less than the significance level

Conclusion: We reject the $H_o$ , thus, there is no sufficient evidence to conclude that there is a significant difference between the SAT math score for students in Pennsylvania and Ohio.

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