Mathematics, 21.12.2020 17:30 gloriuos355

The business college computing center wants to determine the proportion of business students who have personal computers (PCÊ¹s) at home. If the proportion exceeds 25%, then the lab will scale back a proposed enlargement of its facilities. Suppose 200 business students were randomly sampled and 65 have PCÊ¹s at home. Find the rejection region for this test using Î± = 0.01. (Note that this is a right-tailed test). A) Reject H0 if 0 z > 2.33.
B) Reject H0 if 0 z < -2.33.
C) Reject H0 if 0 z > 2.575 or z < -2.575.
D) Reject H0 if 0 z = 2.
Find the test statistic, 0 t , to test the claim about the population mean Î¼ < 6.7 given n = 20, x = 6.3, s = 2.0.
A) -1.233
B) -0.872
C) -1.265
D) -0.894
Determine the test statistic, 0 z , to test the claim about the population proportion p < 0.85 given n = 60 and x = 39.
A) -4.34
B) -1.96
C) -1.85
D) -1.76

Answers: 2

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Answer from: azertyqwerty123

Question 5

correct option is A

Question 6

correct option is D

Question 7

correct option is A

Step-by-step explanation:

Considering question 5

From the question we are told that

The population proportion considered is p = 0.25

The sample size is n = 200

The number that had a personal computer at home is k = 65

The level of significance is $\alpha = 0.01$

The null hypothesis is H_o : p = 0.25

The alternative hypothesis is H_a : p 0.25

Generally from the z-table the critical value of $\alpha = 0.01$ to the right of the curve is

$z_{\alpha } = 2.33$

Generally given that it is a right-tailed test , the rejection region is

z > 2.33

Considering question 6

The sample size is n = 20

The standard deviation is s = 2

The sample mean is $\=x = 6.3$

The population mean $\mu = 6.7$

Generally the test statistics is mathematically represented as

$t = \frac{ \= x - \mu }{\frac{s}{\sqrt{n} } }$

=> $t = \frac{ 6.3 - 6.7 }{ \frac{ 2}{ \sqrt{20} } }$

=> t = -0.894

Considering question 7

The sample size is n = 60

The sample mean is x = 39

The population proportion p = 0.85

Gnerally the sample proportion is mathematically represented as

$\^ p = \frac{x}{n}$

=> $\^ p = \frac{39}{60}$

=> $\^ p = 0.65$

Generally the standard error of this distribution is mathematically represented as

$SE = \sqrt{ \frac{ p(1 - p ) }{ n } }$

=> $SE = \sqrt{ \frac{ 0.85 (1 - 0.85 ) }{ 60 } }$

=> SE = 0.0461

Generally the test statistics is mathematically represented as

$z = \frac{ \^ p - p }{SE}$

=> $z = \frac{ 0.65 - 0.85 }{0.0461}$

=> z = -4.34

Answer from: Quest

the least common denominator is 40

Answer from: Quest

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The business college computing center wants to determine the proportion of business students who hav...