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3 years ago

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A teacher administers a standardized math test to his class of 75 students. The mean score (out of 300 possible points) is 235.

From previous studies, you know the population standard deviation is 28. Using the sample data given, calculate a 95% confidence interval for the population mean.

1 answer:

Ede4ka [16]3 years ago

8 0

Answer:

(228.663 ; 241.337)

Step-by-step explanation:

Given that:

Mean (m) = 235

Standard deviation (s) = 28

α = 95%

Zcritical at 95% = 1.96

Sample size (n) = 75

The confidence interval of the population mean can be obtained using the relation :

Mean ± Error

Error = Zcritical * (s/sqrt(n))

Error = 1.96 * (28/sqrt(75))

Error = 1.96 * 3.2331615

Error = 6.33699654

Error = 6.337

Lower boundary = 235 - 6.337 = 228.663

Upper boundary = 235 + 6.337 = 241.337

(228.663 ; 241.337)

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There is strong believe that language skills of Political science students are greater than students who study Finance. Research

BaLLatris [955]

Answer:

a

The null hypothesis is $H_o : \mu_1 = \mu_2$

The alternative hypothesis $H_a : \mu_1 > \mu_2$

b

$p-value = 0.232$

c

The decision rule is

Fail to reject the null hypothesis

Step-by-step explanation:

From the question we are told that

The value given is

S/N

1 7 5

2 4 3

3 8 7

4 8 8

5 7 9

6 7 5

7 6 5

Generally the sample mean for the first sample is mathematically represented as

$\= x _1 = \frac{\sum x_i }{n}$

=> $\= x _1 = \frac{7 +4 + \cdots + 6}{7}$

=> $\= x _1 = 6.714$

Generally the sample mean for the second sample is mathematically represented as

$\= x _2 = \frac{\sum x_i }{n}$

=> $\= x _2 = \frac{5 + 3+ \cdots + 5}{7}$

=> $\= x _2 = 6$

Generally the sample standard deviation for the first sample is mathematically represented as

$s_1 = \sqrt{\frac{\sum (x_i - \= x_1)^2 }{n-1 } }$

=> $s_1 = \sqrt{\frac{ (7 - 6.714 )^2 +(4 - 6.714 )^2 + \cdots + (6 - 6.714 )^2 }{7-1 } }$

=> $s_1 = 1.905$

Generally the sample standard deviation for the second sample is mathematically represented as

$s_2 = \sqrt{\frac{\sum (x_i - \= x_2)^2 }{n-1 } }$

=> $s_2 = \sqrt{\frac{ (5 - 6.714 )^2 +(3 - 6.714 )^2 + \cdots + (5 - 6.714 )^2 }{7-1 } }$

=> $s_1 = 4.33$

Generally the pooled standard deviation is

$s = \sqrt{\frac{(n_1 - 1 )s_1^2 + (n_2 - 1 )s_2^2}{n_1 + n_2 -2 } }$

=> $s = \sqrt{\frac{(7 - 1 )1.905^2 + (7 - 1 )4.333^2}{7 + 7 -2 } }$

=> $s = 1.766$

The null hypothesis is $H_o : \mu_1 = \mu_2$

The alternative hypothesis $H_a : \mu_1 > \mu_2$

Generally the test statistics is mathematically represented as

$t = \frac{\= x _1 - \= x_2 }{s * \sqrt{\frac{1}{n_1} + \frac{1}{n_2}} }$

=> $t = \frac{6.714 - 6 }{1.766 * \sqrt{\frac{1}{7} + \frac{1}{7}} }$

=> $t = 0.757$

Generally the degree of freedom is mathematically represented as

$df = n_1 + n_2 - 2$

=> $df = 7 + 7 - 2$

=> $df = 12$

From the t distribution table the probability of $t = 0.757$ at a degree of freedom of $df = 12$ is

$t_{ 0.757 , 12} = 0.232$

Generally the p-value is

$p-value = t_{ 0.757 , 12} = 0.232$

From the values obtained we see that $p-value > \alpha$ hence

The decision rule is

Fail to reject the null hypothesis

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3 years ago

gordan is twice as old as tony was when gordan was as old as tony is now. combined age of gordan and tony is 112 years. how old

Neporo4naja [7]

Gordan is 67 and Tony is 45 years old

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3 years ago

Read 2 more answers

Solve for m -mk-90>85

loris [4]

First add 90 to both sides) -mk>85+90simplify 85+90 to 175) -mk>175divide both sides by K) -m>175/kmultiply both sides by -1) m<-175/k
YOUR ANSWER IS
M<-175/K
hope l helped today l was stuck on the same question doing part 2 of alg exam , and l came through your question l hope it's not too late :)

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3 years ago

The area of a 12-cm-wide rectangle is 288 cm^2 what is its length?

densk [106]

Answer:

24cm

Step-by-step explanation:

The area of the rectangle is length × breadth. You already know the area and the breadth, so you can find the length.

288cm² = length × 12cm

length = 288cm² ÷ 12cm

= 24cm

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2 years ago

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Gala2k [10]

Answer:

29°, 58°, and 93°

Step-by-step explanation:

If the angles opposite are equal, the sides are equal. In order to have three different side lengths, you must have <em>three different angles</em>.

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