final orms

In general the null and alternative hypotheses are

mutually exclusive

The R2 of a multiple regression of y on x1 and x2 measures the ______

percentage of the total variation in y that is explained by the sample regression

What is the most typical form of a calculated confidence interval?

point esstimate +/_ error

a 90% confidence interval is constructed for the population mean. If a 95% confidence interval had been constructed instead ( everything else remaining the same), the width of the interval would have been_____ and the probability of making an error would have been _______

wider, smaller

a university is interested in promoting graduates of its honors program by establishing the mean GPA of these graduates exceeds 3.5. A sample of 36 honor students is taken and is found to have a mean GPA equal to 3.6. The population standard deviation is assumed to equal .4. the value of the test statistic is?

z=1.50

we draw a random sample of size 36 from a population with standard deviation of 3.5. if the sample mean is 27. what is the 95% confidence interval for the population mean?

(25.8567, 28.1433)

In an examination of purchasing patterns of shoppers, a sample of 16 shoppers revealed that they spent, on average. $54 per hour of shopping. based on previous years, the population standard deviation is thought to be $21 per hour of shopping. Assuming that the amount spent per hour of shopping is normally distributed, find a 90% confidence interval for the mean amount

(45.36, 62.64)

A sample regression equation is given by y=-100+.5x if x=20 the predicted value of y is ______

-90

A company decided to test the hypothesis that the average time a company's employees are spending to check their private e-mails at work is more than 13 minutes. A random sample of 25 employees were selected and they averaged 13.6 min. it is believed that the population standard deviation is 1.6 min. The A is set to .05 the p-value for this test would be

.0300

what is the za/2 for a 95% confidence interval of the population mean?

1.96

The daily revenue from the sale of fried dough at a local street vendor in boston is known to be normally distributed with a known standard deviation of $120. the revenue on each of the last 25 days is noted, and the average is computed as $550. Construct a 95% confidence interval for the population mean of the sale of fried dough by this vendor

550 +/_ 1.96(120/5)

For a given confidence level and sample size, which of the following is true in the interval estimation of the population mean when the population standard deviation sigma is known?

As the population standard deviation gets larger, the interval estimation gets wider.

The alternative hypothesis typically________

Contests the status quo, for which a corrective action may be required

when testing the overall significance of the regression model at the 5% level given a critical value of F0.05, (2,20)= 3.49 the decision and conclusion are __________

Do not reject H0 and conclude that the explanatory variables are not jointly significant

The owner of a large car dealership believes that the financial crisis decreased the number of customers visiting her dealership. The dealership has historically had 800 customers per day. The owner takes a sample of 100 days and finds the average number of customers visiting the dealership per day was 750. Assume the population standard deviation is 350. At the 5% significance level, what is your decision and conclusion?

Do not reject H0: we cannot conclude the mean number of customers visiting the dealership is significantly less then 800

Consider the following sample linear regression model: y=b0+b1x+e when determining whether x significantly influences y. the null hypothesis takes the form _________

H0:b1=0

The owner of a large car dealership believes that the financial crisis decreased the number of customers visiting her dealership. The dealership has historically had 800 customers per day. The owner takes a sample of 100 days and finds the average number of customers visiting the dealership per day was 750. Assume the population standard deviation is 350. To determine whether there has been a decrease in the average number of customers visiting the dealership daily, the appropriate hypothesis are

H0:u</800 and Ha:u>800

a university is interested in promoting graduates of its honors program by establishing the mean GPA of these graduates exceeds 3.5. A sample of 36 honor students is taken and is found to have a mean GPA equal to 3.6. The population standard deviation is assumed to equal .4. to establish whether the mean GPA exceeds 3.5 the appropriate hypotheses are _______________

Ho:u</_3.5 and Ha>3.5

When testing the overall significance of the regression model using the p-value approach at the 5% level, the decision and conclusion are________

Reject H0; we can conclude that at least one of the explanatory variables is significantly related to the response variable

A type 1 error occurs when we ____________

Reject the null hypothesis when it is actually ture

What is the purpose of calculating a confidence interval?

To provide a range of values that, with a certain measure of confidence, contains the population parameter of interest

Consider the sample regression equation y=12+3x1-5x2+7x3-2x4 when x1 increases by 1 united and x2 increases by 2 units, While x3 and x4 remain unchanged, what change would you expect in the predicted y value?

decrease by 7

an analyst takes a random sample of 25 firms in the telecommunications industry and constructs a confidence interval for the mean return for the prior year. Holding all else constant, if he increased the sample size to 30 firms, how are the standard error of the mean and the width of the confidence interval affected?

decreases, becomes narrower

In regression, multicollinerity is considered problematic when two or more explanatory values are________

highly correlated

To test if the mean IQ of employees in an organization is greater then 100, a sample of 30 employees is taken and the value of the test statistic is computed as t29=2.42 if we choose a 5% significance level, what is your decision and conclusion

reject the null hypothesis; we can conclude that the mean IQ is greater then 100

The standard error of the estimate is a measure of the standard deviation of the ____

residuals

The null hypothesis in a hypothesis test refers to ________

the default state of nature of status quo

The Ages of MBA students at a university are normally distributed with a known population variance of 10.24. Suppose you are asked to construct a 95% confidence interval for the population mean age if the mean of a sample of 36 students is 26.5 years. If a 99% confidence interval is constructed instead of the 95% confidence interval for the population mean, then ______________________________

the resulting margin of error will increase the risk of reporting an incorrect interval will increase

consider the following simple linear regression model y=b0+B1x+E B0 and B1 are

the unknown regression parameters

Multicollinearity is suspected when?

there is a high R2 coupled with insignificant explanatory variables.