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Elan Coil [88]
3 years ago
6

Two researchers conducted a study in which two groups of students were asked to answer 42 trivia questions from a board game. Th

e students in group 1 were asked to spend 5 minutes thinking about what it would mean to be a​ professor, while the students in group 2 were asked to think about soccer hooligans. These pretest thoughts are a form of priming. The 200 students in group 1 had a mean score of 21.9 with a standard deviation of 3.4​, while the 200 students in group 2 had a mean score of 19.8 with a standard deviation of 3.5.
(a) Determine the 95% confidence interval for the difference in scores μ1 - μ2.
Mathematics
1 answer:
Verizon [17]3 years ago
5 0

Answer:

(21.9-19.8) -1.966\sqrt{\frac{3.4^2}{200} +\frac{3.5^2}{200}}= 1.422

(21.9-19.8) -1.966 \sqrt{\frac{3.4^2}{200} +\frac{3.5^2}{200}}= 2.778

And we are 95% confident that the true difference means are between 1.422 \leq \mu_1 -\mu_2 \leq 2.778

Step-by-step explanation:

We know the following info:

\bar X_1 = 21.9 sample mean for group 1

\bar X_2 = 19.8 sample mean for group 2

s_1 = 3.4 sample standard deviation for group 1

s_2 = 3.5 sample standard deviation for group 2

n_1 = 200 sample size group 1

n_2 = 200 sample size group 2

We want to find a confidence interval for the difference of means and the correct formula to do this is:

(\bar X_1 -\bar X_2) \pm t_{\alpha/2} \sqrt{\frac{s^2_1}{n_1} +\frac{s^2_2}{n_2}}

Now we just need to find the critical value. The confidence level is 0.95 then the significance is 1-0.95 =0.05 and \alpha/2 =0.025. The degrees of freedom are given by:

df= n_1 +n_2 -2= 200+200-2= 398

The critical value for this case would be :t_{\alpha/2}=1.966  

And replacing into the confidence interval formula we got:

(21.9-19.8) -1.966\sqrt{\frac{3.4^2}{200} +\frac{3.5^2}{200}}= 1.422

(21.9-19.8) -1.966 \sqrt{\frac{3.4^2}{200} +\frac{3.5^2}{200}}= 2.778

And we are 95% confident that the true difference means are between 1.422 \leq \mu_1 -\mu_2 \leq 2.778

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The coordinates of point 7 are given. The midpoint of ST is (5. - 8). Find the coordinates of point S.
Mamont248 [21]

Answer:

S(0, 2)

Step-by-step explanation:

Midpoint Formula: (\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2} )

Step 1: Plug in known variables

5 = (10 + x)/2

-8 = (18 + y)/2

Step 2: Solve

10 = 10 + x

x = 0

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Step 3: Write coordinates

(0, 2)

4 0
3 years ago
Do rational expressions contain logarithmic functions? A. always B. sometimes C. never
bazaltina [42]

The right answer is C. never


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3 0
3 years ago
Read 2 more answers
Coffee table is 20% odd the original price of $115. If there is 7.5% sales tax, what is the final price of the coffee table?
netineya [11]
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The final price of the coffee table is $98.90. 

Hope this helps! 
3 0
3 years ago
Write the answer to each problem in terms of the variable.
Liono4ka [1.6K]
(34 - R) will be the <span>expression of the other number</span>.
3 0
3 years ago
6.4934 rounded to 6.493
iris [78.8K]

Answer:

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Step-by-step explanation:

4 0
3 years ago
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