Statistics Final

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An interval estimate may or may not contain the true value of the parameter being estimated

True

The confidence level of an interval estimate of a parameter is the probability that the interval estimate will contain the parameter.

True

The term Z ∝⁄2 ( σ/√n) describes

maximum error of estimate

the formula for the confidence interval of the mean for a specific ∝ is

x̄ - z ∝⁄2 ( σ/√n)<μ<x̄ + z ∝⁄2 ( σ/√n)

What value of z ∝⁄2 is used in confidence interval shown below (90%=μ)

1.65

A sample of 35 different payroll departments found that employees worked an average of 240.6 days a year. If the population standard deviation is 18.8 days, find the 90% confidence interval for the average number of days μ worked by all employees who are paid through payroll departments

235.4<μ<245.8

A student looked up the number of years served by 35 of the more than 100 supreme court justices. The average number of years served by those 35 justices was 13.8. If the standard deviation of the entire population is 7.3 year, find the 95% confidence interval for the average number of years served by all supreme court justices.

11.4<μ<16.2

A study of 55 apple trees showed that the average number of apples per tree was 625 the standard deviation of the population is 100. Which of the following is the 90% confidence interval for the mean number of apples per tree for all trees.

481<μ<569

A study of 35 white mice showed that their average weight was 4.2 ounces. The standard deviation of the population is 0.6 ounces. Which of the following is the 98% confidence interval for the mean weight per white mouse.

5.04<μ<5.36

What is the value of ∝ used in describing the confidence interval shown below (98%)

0.02

Identify the degree of confidence displayed in the confidence interval shown below (∝⁄2=0.05 and ∝⁄2=0.05)

90%

The t-distribution must be used when the sample size is greater than 30 and the variable is normally or approximately normally distributed.

False

The t-distribution has a variance that is greater than one

True

In a study using 13 samples, and in which the population variance is unknown, the distribution that should be used to calculate confidence intervals is

a t-distribution with 12 degrees of freedom

Find t∝⁄2 when n=12 for the 90% confidence interval for the mean

1.80

The prices (in dollars) for a graphing calculator are shown below for 8 online vendors. Estimate the true mean price for this particular calculator with 95% confidence (124, 129,130, 155, 134, 158, 150, 142)

136.6<μ<147.7

The winning team's score in 11 high school basketball games was recorded. If the sample mean is 72.3 points and the sample standard deviation is 12.0 points, find the 98% confidence interval of the true mean

52.1<μ<68.5

In a study of 100 new cars, 27 are white. Find p̂ and q^ where p̂ is the proportion of new cars that are white.

p̂=0.32, q^=0.68

A random sample of 100 voters found that 44% were going to vote for a certain candidate. Find the 99% limit for the population proportion of voters who will vote for the candidate.

31.2%<p<56.8%

A random sample of 70 printers discovered that 20 of them were being used in small businesses. Find the 99% limit for the population proportion of printers that re used in small businesses.

0.146<p<0.425

A report states that 42% of home owners has a vegetable garden. How large a sample is needed to estimate the true proportion of home owners who have vegetable gardens to within 6% with 95% confidence?

260

A college believes that 26% of applicants to that school have parents who have remarried. How large a sample is needed to estimate the true proportion of students who have parents who have remarried within 6% points with 99% confidence.

356

If p̂ is equal to 0.85 then q^ is equal to

0.15

the area under each chi square distribution is equal to

1.00

In order to find confidence interval for variances and standard deviation, one must assume that the variable is

normally distributed

What is the value for x^2 left for a 95% confidence interval n=18

7.564

What is the value for x^2 right for a 98% confidence interval when n=12

24.725

Find the values for x^2 left and x^2 right when ∝=0.05 and n=17

6.908 and 28.845

Are the following statements Ho:=9 and H1: ≠9 valid null and alternative hypothesis Ho:λ=9 and H1:λ<9 a valid pair of null and alternative hypothesis

No, there are no parameters contained in these statements

Are the following statements Ho:λ=9 and H1:λ<9 a valid pair of null and alternative hypothesis

Yes, the null hypothesis specifies an equality and alternative specifies a difference

The numerical value obtained from a statistical test is called the

test value

A type I error occurs if one rejects the null hypothesis when it is

True

A type II error occurs if one does not reject the null hypothesis when it is

False

The probability of a type I error is represented by which of the following symbols?

A right tailed test is used when H0: μ≥k

False

Which type of alternative hypothesis is used in the figure below

H1: μ > k

In performing a hypothesis test, one should decide whether to reject or not reject the null H0 before summarizing the results.

True

Using the z table, find the critical value for an ∝=0.09 two tailed test

+ or - 1.69

Using the z test, find the critical value for an ∝=0.015 left tailed test

-2.17

Using the z-table, determine the critical values for a two tailed test when ∝=0.03

+ or - 2.17

For the conjecture " the average rent of an apartment is more than $950 per month," the alternative hypothesis is

the average rent of an apartment is greater than $950 per month.

For conjecture "the average weight of a cuckoo bird is less than 2.2 pounds", the null and alternative hypothesis are

H0: the average weight of a cuckoo bird is equal to 2.2 pounds H1: the average weight of a cuckoo bird is less than 2.2 pounds

If the sample mean is 7, the hypothesized population mean is 6 and the population standard deviation is 2, compute the test value needed for the z test

0.50

When conducting a two tailed z test with ∝=0.01, the test value was computed to be 2.07 the decision would be to not reject the null hypothesis.

True

If the sample mean is 9 the hypothesized population mean is 10 and the population standard deviation is 3 compute the test value needed for the z test.

- 0.33

At a certain university, the average cost of books was $320 per student last semester and the population standard deviation was $85. This semester a sample of 40 students revealed an average cost of books of $345 per student. The dean of students believes that the costs are greater this semester. What is the test value for this hypothesis?

1.86

The average greyhound can reach a top speed of 18.9 meters per second. A particular greyhound breeder claims her dogs are faster than the average greyhound. A sample of 40 of her dogs ran on average, 19.5 meters per second with a population standard deviation of 1.5 meters per second. With ∝ =0.05 is her claim correct?

Yes, because the test value 2.53 falls in the critical region

What is the critical value for a two tailed t test when ∝ =0.02 and n=19?

2.552

What is the critical value for a right tailed t test when ∝ =0.025 and n=13?

2.179

Find the P-value for the test value t=1.61, n=15, right tailed

0.0649

A recent study of business travelers claims they spend an average of $41.00 per day on meals. As a test of this claim, a random sampling of 16 business travelers found they had spent an average of $45.00 per day with a standard deviation of $3.65.What are the critical values for a two tailed t test of this claim with ∝ =0.05?

+ or - 2.131

According to Beautiful Bride magazine the average age of a groom is now 26.2 years. A sample of 16 prospective grooms in Chicago revealed that their average age was 26.6 years with a standard deviation of 5.3 years. What is the test value for a t test of claim?

0.30

At certain university, the average attendance at basketball games has been 3225. This year the attendance for the first 12 games has been 2815 with a standard deviation of 635. The athletic director claims that the attendance is the same as last year. If ∝=0.05 what are the critical values for this two tailed t test?

+ or - 2.201

At certain university, the average attendance at basketball games has been 3225. Due to the dismal showing of the team this year, the attendance for the first 8 games has averaged only 2915 with a standard deviation of 535. The athletic director claims that the attendance is the same as last year. What is the test value needed to evaluate the claim?

-2.17

A political strategist claims that 55% of voters in Madison County support his candidate. In a poll of 300 randomly selected voters, 147 of them support strategist's candidate. At ∝ =0.05 is the political strategist claim warranted?

No, because the test value -2.09 is in the critical region

A scientist claims that only 64% of geese in his area fly south for the winter. He tags 55 random geese in the simmer and finds that 17 of them do not fly south in the winter. If ∝ 0.05 is, the scientist belief warranted?

Yes because the test value 0.79 is in the noncritical region

If the probability of a type II error in a hypothesis test is =0.30 and ∝ =0.05 the power of this test is

0.70

If the null hypothesis H0: μ=15 is not rejected at ∝ =0.05 when a mean of 15 is obtained from a random sample, one could say that the

95% confidence interval for the population mean contains the value 16

Assume that a 99% confidence interval for the mean is 14.5 < μ <17.5. the null hypothesis H0: μ=13.0 at ∝ =0.01would

be rejected because 14 is less than 16

Assume that a 95% confidence interval for the mean is 11.5 < μ <16. the null hypothesis H0: μ=13.0 at ∝ =0.05 would

be rejected because 14 is between 13.5 and 15

If the null hypothesis H0: μ=14.0 is rejected at ∝ =0.01when a mean of 19 is obtained from a random sample, one could also say that the

99% confidence interval for the population mean does not contain the value 16.

If the test value for the difference between the means of two large samples is 2.57 when the critical value is 1.96 what decision would be made?

Reject the null hypothesis (picture)

Test value for the difference between the means of two large samples is 1.43 the CV is 1.96 the null hypo. shouldn't be rejected.

True (picture)

Consider the null hypothesis H0: μ1- μ2 =0. If the CI for μ1- μ2 does not contain 0 the null hypothesis shoe be rejected.

True

Comparing the means of samples from two normally distributed pop., if the samples are independent and the pop. variances are known, the z test can be used.

True

Mauricio Cruz a wine merchant for Cruz's Spirits Emporium, wants to determine if the average price of imported wine is less than the average price of domestic wine he obtained data shown in the table below. Imported wine x̄1=$7.03 S1 =$2.31 n=15 Domestic Wine x̄1=$9.78 S1 =$3.62 n=16 The null hypothesis is

H0: μ1= μ2

Which of the following represent dependent samples i. Life spans of pairs of sibling's ii. Life spans of randomly selected pairs of people iii. Life spans of pairs of mother and daughters.

I and III

A medical researcher is interested in whether patients left arms or right arms are longer. If 14 patients participate in this study, how many degrees of freedom should the researcher use when finding the critical value for a t test?

13

The critical value for a left tailed t test for dependent samples is ... when there are 7 degrees of freedom and ∝ =0.025

-2.365

A positive relationship exists when both variables increase or decrease at the same time

True

The two variables in a scatter plot are called the

independent variable and dependent variable

Determine the type of relationship shown in (picture)

Positive

Daniel Wiseman for Gres Trans Corp. wants to determine if the flow rate of particular material changes with different changes in temperature. The data plotted in (picture) what type of relationship exists between the flow rate and the change in temperature.

There is no relationship

A correlation coefficient of 0.961 would mean that the values of x increase as the values of y decrease

False

When r is not significantly different from 0, the best predictor of y is the .... of the data values of y

mean

A regression line can be used to show trends in data

True

A regression line was calculated as y1 =9.7-3.2x. the slope of this line is -3.2

True

An equation of a regression line is y1 =4.6+3.2x what is the intercept of this line.

4.6

If the equation for the regression line is y1 =-8x+7 then the slope of this line is

-8

If the equation for the regression line is y1 =-6x+7 then the intercept of this line is

7

If the equation for the regression line is y1 =7x-5 then the value of x=3 will result in a predicted value for y of

16

If the equation for the regression line is y1 =6x+5 then the value of x= -2will result in a predicted value for y of

-7

What is the value of y1 when x=3 if the equation of the regression lines is y1 =23.1-3.8x?

11.7

If the correlation coefficient is 0.790 what is the variation?

62.4%

If the correlation coefficient is 0.930 what is the unexplained variation?

13.5%

A correlation coefficient r was calculated to be 0.830 the coefficient of nondetermination would be 0.170

False

A correlation coefficient r was calculated to be 0.610 the coefficient of determination would be approximately

0.372

Confidence level: 90%

1.64

Confidence level:95%

1.96

Confidence level: 99%

2.58

Confidence level: 80%

1.28

Population mean

μ

Sample mean

Population standard deviation

σ

Sample standard deviation

s

Population Variance

σ²

Sample Variance

Population Correlation

ρ

Sample Correlation

r

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