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suter [353]
3 years ago
6

Independent random samples taken on two university campuses revealed the following information concerning the average amount of

money spent on textbooks during the fall semester.University A University BSample Size 50 40Average Purchase $280 $250Standard Deviation $20 $23At * = .05, test to determine if, on the average, students at University A spend more on textbooks then the students at University B
Mathematics
2 answers:
love history [14]3 years ago
8 0

Answer:

p_v =P(t_{88}>6.960) =2.91x10^{-10}

So with the p value obtained and using the significance level given \alpha=0.05 we have p_v so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the mean of the group A is significantly lower than the mean for the group B.  

Step-by-step explanation:

The statistic to test the hypothesis is given by this formula:

t=\frac{(\bar X_A-\bar X_B)-(\mu_{A}-\mu_B)}{\sqrt{\frac{s_A^2}{n_A}}+\frac{s_B^2}{n_B}}

Where t follows a t distribution with n_1+n_2 -2 degrees of freedom

The system of hypothesis on this case are:

Null hypothesis: \mu_A \leq \mu_B

Alternative hypothesis: \mu_A >\mu_B

Or equivalently:

Null hypothesis: \mu_A - \mu_B \leq 0

Alternative hypothesis: \mu_A -\mu_B>0

Our notation on this case :

n_A =50 represent the sample size for group A

n_B =40 represent the sample size for group B

\bar X_A =280 represent the sample mean for the group A

\bar X_B =250 represent the sample mean for the group B

s_A=20 represent the sample standard deviation for group A

s_B=23 represent the sample standard deviation for group B

And now we can calculate the statistic:

t=\frac{(280 -250)-(0)}{\sqrt{\frac{20^2}{50}}+\frac{23^2}{40}}=6.511

Now we can calculate the degrees of freedom given by:

df=50+40-2=88

And now we can calculate the p value using the alternative hypothesis:

p_v =P(t_{88}>6.960) =2.91x10^{-10}

So with the p value obtained and using the significance level given \alpha=0.05 we have p_v so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the mean of the group A is significantly lower than the mean for the group B.  

riadik2000 [5.3K]3 years ago
8 0

Answer:

Step-by-step explanation:

Download docx
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