Shown below is a portion of a computer output for a regression analysis relating Y (dependent variable) and X (independent variable).ANOVA   dfSSRegression  1115.064Residual13  82.936Total      CoefficientsStandard ErrorIntercept15.5321.457x –1.1060.261​a.Perform a t test using the p-value approach and determine whether x and y are related. Let α = 0.05.b.Using the p-value approach, perform an F test and determine whether x and y are related.c.Compute the coefficient of determination and fully interpret its meaning. ​

The price of a particular brand of jeans has a mean of $37.99 and a standard deviation of $7. A sample of 49 pairs of jeans is selected. Use Excel to answer the following questions:a.What is the probability that the sample of jeans will have a mean price less than $40?b.What is the probability that the sample of jeans will have a mean price between $38 and $39?c.What is the probability that the sample of jeans will have a mean price within $3 of the population mean? ​

Using α = 0.04, a confidence interval for a population proportion is determined to be 0.65–0.75. If the level of significance is decreased, the interval for the population proportion _____.

Given below are seven observations collected in a regression study on two variables, x (independent variable) and y (dependent variable). xy  212  39  68  77  86  75  92 ​a.Develop the least squares estimated regression equation.b.At 95% confidence, perform a t test and determine whether the slope is significantly different from zero. c.Perform an F test to determine whether the model is significant. Let α = 0.05.d.Compute the coefficient of determination.​

In order to estimate the difference between the yearly incomes of marketing managers in the East and West of the United States, the following information was gathered: EastWest n1 = 40n2 = 45  = 72 (in $1000s) = 78 (in $1000s) s1 = 6 (in $1000s)s2 = 8 (in $1000s)​a.Develop an interval estimate for the difference between the average yearly incomes of the marketing managers in the East and West. Use α = 0.05. b.At 95% confidence, use the p-value approach and test to determine if the average yearly income of marketing managers in the East is significantly different from the West. ​

A company has recorded data on the weekly sales for its product (y) and the unit price of the competitor’s product (x). The data resulting from a random sample of seven weeks follows. Use Excel to:a.Compute a 95% confidence interval for expected sales for all weeks when the competitor’s price is 0.30.b.Compute a 95% prediction interval for sales for a week when the competitor’s price is 0.30.   WeekPriceSales  10.3320  20.2514  30.4422  40.4021  50.3516  60.3919  70.2915 ​​

A random sample of 100 credit sales in a department store showed an average sale of $120.00. From past data, it is known that the standard deviation of the population is $40.00.a.Determine the standard error of the mean.b.With a 0.95 probability, determine the margin of error.c.What is the 95% confidence interval of the population mean?​

For which of the following values of p is the value of p(1 − p) maximized?

Nancy believes that the average running time of movies is equal to 140 minutes. A sample of four movies was taken, and the following running times were obtained. Assume the distribution of the population is normally distributed. 150150180170 ​a.State the null and alternative hypotheses.b.Using a critical value, test the hypothesis at the 10% level of significance.c.Using a p-value, test the hypothesis at the 10% level of significance.d.Using a confidence interval, test the hypothesis at the 10% level of significance.e.Could a Type II error have been committed in this hypothesis test?​

If the standard deviation of the lifetimes of vacuum cleaners is estimated to be 300 hours, what sample size must be selected in order to be 97% confident that the margin of error will not exceed 40 hours?