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In a city known for many tech start-ups, 311 of 800 randomly selected college graduates with outstanding student loans currently owe more than $50,000. In another city known for biotech firms, 334 of 800 randomly selected college graduates with outstanding student loans currently owe more than $50,000. Perform a two-proportion hypothesis test to determine whether there is a difference in the proportions of college graduates with outstanding student loans who currently owe more than $50,000 in these two cities. Use α=0.05. Assume that the samples are random and independent. Let the first city correspond to sample 1 and the second city correspond to sample 2. For this test: H0:p1=p2; Ha:p1≠p2, which is a two-tailed test. The test results are: z≈−1.17 , p-value is approximately 0.242

Answers

Answer 1

Answer:

Answer:

Null hypothesis: $p_(1) - p_(2)=0$

Alternative hypothesis: $p_(1) - p_(2) \neq 0$

$z=\frac{0.389-0.418}{\sqrt{0.403(1-0.403)((1)/(800)+(1)/(800))}}=-1.182$

$p_v =2*P(Z<-1.182)=0.2372$

Comparing the p value with the significance level given $\alpha=0.05$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can say that we don't have significant difference between the two proportions.

Step-by-step explanation:

1) Data given and notation

$X_(1)=311$ represent the number college graduates with outstanding student loans currently owe more than $50,000 (tech start-ups)

$X_(2)=334$ represent the number college graduates with outstanding student loans currently owe more than $50,000 ( biotech firms)

$n_(1)=800$ sample 1

$n_(2)=800$ sample 2

$p_(1)=(311)/(800)=0.389$ represent the proportion of college graduates with outstanding student loans currently owe more than $50,000 (tech start-ups)

$p_(2)=(334)/(800)=0.418$ represent the proportion of college graduates with outstanding student loans currently owe more than $50,000 ( biotech firms)

z would represent the statistic (variable of interest)

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

$\alpha=0.05$ significance level given

2) Concepts and formulas to use

We need to conduct a hypothesis in order to check if is there is a difference in the two proportions, the system of hypothesis would be:

Null hypothesis: $p_(1) - p_(2)=0$

Alternative hypothesis: $p_(1) - p_(2) \neq 0$

We need to apply a z test to compare proportions, and the statistic is given by:

$z=\frac{p_(1)-p_(2)}{\sqrt{\hat p (1-\hat p)((1)/(n_(1))+(1)/(n_(2)))}}$ (1)

Where $\hat p=(X_(1)+X_(2))/(n_(1)+n_(2))=(311+334)/(800+800)=0.403$

3) Calculate the statistic

Replacing in formula (1) the values obtained we got this:

$z=\frac{0.389-0.418}{\sqrt{0.403(1-0.403)((1)/(800)+(1)/(800))}}=-1.182$

4) Statistical decision

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

$p_v =2*P(Z<-1.182)=0.2372$

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Answers

Final answer:

To solve for x in a triangle with side lengths of 67, 29, and x, we can use the Law of Cosines. The value of x is approximately 47.6.

Explanation:

To solve for x in the given triangle with side lengths 67, 29, and x, we can use the Law of Cosines. The Law of Cosines states that for any triangle with side lengths a, b, and c and angle C opposite side c, the following equation holds true: c^2 = a^2 + b^2 - 2ab*cos(C). In this case, we can substitute the given values into the equation and solve for x. Let's calculate it:

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x^2 = 4489 + 841 - 3886cos(C)

Solving for x, we find that x is approximately 47.6.

Learn more about Law of Cosines here:

brainly.com/question/21634338

#SPJ12

Answer:

84°

Step-by-step explanation:

Because every triangle has a combined side length of 180°

67+29=96°

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Answers

Answer:

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Step-by-step explanation:

divide both by two for its simplest form

Answer:4/7

Step-by-step explanation

Divide both the numerator and denominator by 2

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Answers

Step-by-step explanation:

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Answers

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Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

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