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# Z-Score, Null Hypothesis, and Statistic Value

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1-
A company that sells an online course aimed at helping high-school students improve their SAT scores has claimed that SAT scores will improve by more than 90 points on average if students successfully complete the course. To test this, a national school counseling organization plans to select a random sample of n = 100 students who have previously taken the SAT test. These students will take the company's course and then retake the SAT test. Assuming that the population standard deviation for improvement in test scores is thought to be 30 points and the level of significance for the hypothesis test is 0.05, find the critical value in terms of improvement in SAT points, which would be needed prior to finding a beta.

A Reject the null if SAT improvement is > 95.88 points.

B Reject the null if SAT improvement is < 85.065 points.

C Reject the null if SAT improvement is > 95 points.

D Reject the null if SAT improvement is > 94.935 points.

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2-
It is believed that the SAT scores for students entering two state universities may have different standard deviations. Specifically, it is believed that the standard deviation at University A is greater than the standard deviation at University B. To test this using an alpha = 0.05 level, a sample of 14 student SAT scores from University A was selected and a sample of 8 SAT scores from University B was selected. The following sample results were observed:
University A University B
= 1104 = 1254
s = 134 s = 108
Based on this information, what is the value of the test statistic?
(1point)

a 1.5394

b 1.2407

c 0.6496

d None of the above.

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3-
The asking price for homes on the real estate market in Baltimore has a mean value of \$286,455 and a standard deviation of \$11,200. The mean and standard deviation in asking price for homes in Denver are \$188,468 and \$8,230, respectively. Recently, one home sold in each city where the asking price for each home was \$193,000. Assuming that both distributions are bell-shaped, which of the following statements is true?
(1point)
A The Denver home has a higher standard z-value.

B The Baltimore home has the higher standard z-value.

C The coefficient of variation for Denver is less than for Baltimore.

D Both cities have the same coefficient of variation.

##### Solution Summary

The solution determines the z-score, null hypothesis and statistic value.

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1-
A company that sells an online course aimed at helping high-school students improve their SAT scores has claimed that SAT scores will improve by more than 90 points on average if students successfully complete the course. To test this, a national school counseling organization plans to select a random sample of n = 100 students who have previously taken the SAT test. These students will take the company's course and then retake the SAT test. Assuming that the population standard deviation for improvement in test scores is thought to be 30 points and the level of significance for the hypothesis test is 0.05, find the critical value in terms of improvement in SAT points, which would be needed prior to finding a ...

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