Mathematics, 14.04.2020 16:37 mirandatorres2601

You are testing the claim that the mean GPA of night students is different from the mean GPA of day students. You sample 30 night students, and the sample mean GPA is 2.34 with a standard deviation of 0.456. You sample 25 day students, and the sample mean GPA is 2.59 with a standard deviation of 0.482. Test the claim using a 10% level of significance. Assume the sample standard deviations are unequal and that GPAs are normally distributed.

Answers: 2

Show answers

Answers

Answer from: ste78

$t=\frac{2.59-2.34}{\sqrt{\frac{0.482^2}{25}+\frac{0.456^2}{30}}}}=1.963$

$df=n_{A}+n_{B}-2=30+25-2=53$

$p_v =2*P(t_{(53)}1.963)=0.0549$

If we compare the p value and the significance level given $\alpha=0.1$ we see that p_v so we can conclude that we have enough evidence to reject the null hypothesis, and we can conclude that the two means are different at 10% of significance.

Step-by-step explanation:

Data given and notation

$\bar X_{A}=2.34$ represent the mean for the sample of night students

$\bar X_{B}=2.59$ represent the mean for the sample of day students

$s_{A}=0.456$ represent the sample standard deviation for the sample of night students

$s_{B}=0.482$ represent the sample standard deviation for the sample of day students

$n_{A}=30$ sample size selected for the night students

$n_{B}=25$ sample size selected for the day students

$\alpha=0.1$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

p_v represent the p value for the test (variable of interest)

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the two means are equal or no, the system of hypothesis would be:

Null hypothesis: $\mu_{A} = \mu_{B}$

Alternative hypothesis: $\mu_{A} \neq \mu_{B}$

If we analyze the size for the samples both are <= than 30 and we don't know the population deviations, for this case is better apply a t test to compare means, and the statistic is given by:

$t=\frac{\bar X_{B}-\bar X_{A}}{\sqrt{\frac{s^2_{B}}{n_{B}}+\frac{s^2_{A}}{n_{A}}}}$ (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other".

Calculate the statistic

We can replace in formula (1) the info given like this:

$t=\frac{2.59-2.34}{\sqrt{\frac{0.482^2}{25}+\frac{0.456^2}{30}}}}=1.963$

P-value

The first step is calculate the degrees of freedom, on this case:

$df=n_{A}+n_{B}-2=30+25-2=53$

Since is a two sided test the p value would be:

$p_v =2*P(t_{(53)}1.963)=0.0549$

Conclusion

Answer from: Quest

y = - 6

step-by-step explanation:

given the point (- 2, y) lies on the graph then it is a solution of it's equation.

substitute x = - 2 into the equation for value of y

y = 3(- 2) = 3 × - 2 = - 6

the point on the graph is (- 2, 6)

Answer from: Quest

The answer would be a

Another question on Mathematics

Mathematics, 21.06.2019 15:30

The diameter of a circular chip is doubled to use in a new board game. the area of the new chip will be

Answers: 2

Answer

Mathematics, 21.06.2019 16:00

Apatient is to take 60 mg of an antibiotic on day 1, take 45mg on days 2 and 3, take 30mg on days 4 and 5 and take 15 mg on days 6 and 7. how many total mg will the patient take?

Answers: 1

Answer

Mathematics, 22.06.2019 02:50

The graph of f(x) shown below has the same shape as the graph of g(x)=x^3-x^2 but it is shifted to the left 2 units what is its equation

Answers: 2

Answer

Mathematics, 22.06.2019 03:00

Alocal restaurant advertises that the mode cost of their most popular meals is $8. if the costs of their most popular meals are $7, $8, $8, $12, $13, $15, $17, $18, and $20, which word or phrase best describes this kind of advertising? accurate inaccurate accurate, but misleading inaccurate and misleading

Answers: 1

Answer

You know the right answer?

You are testing the claim that the mean GPA of night students is different from the mean GPA of day...

Questions

Mathematics, 18.03.2021 08:20

The first year Eleanor organized a fund-raising event, she invited 30 people. For each of the next 5 years, she invited double the number of p...