Which statement best describes statistics?

  ​ Coefficients Standard Error t Stat P-value ​ Intercept -9929.811142 24657.33026 -0.402712339 0.703800734 ​ Square Feet 16.0452627 23.04757868 0.696179973 0.517343052 ​ Number of Bedrooms 45079.68306 15349.88995 2.936808226 0.032376169 ​ Age -668.5304253 2038.159618 -0.328006904 0.756196359 ​   The data above was calculated relating square footage, number of bedroom, and age to the response variable, price of a home.  What are the null and alternative hypotheses when using the t test statistic? (Subscripts are not needed, for example you can type x1 as if the 1 was the subscript)

  ​ Coefficients Standard Error t Stat P-value ​ Intercept -9929.811142 24657.33026 -0.402712339 0.703800734 ​ Square Feet 16.0452627 23.04757868 0.696179973 0.517343052 ​ Number of Bedrooms 45079.68306 15349.88995 2.936808226 0.032376169 ​ Age -668.5304253 2038.159618 -0.328006904 0.756196359 ​   The data above was calculated relating square footage, number of bedroom, and age to the response variable, price of a home.  What is the adjusted coefficient of determination? What is it adjusted for?

                                                   Nurses (X)            Patient Falls (Y)Mean                                            40                        200Standard Deviation                  15                        50Use the data above.Research has found that the correlation between number of nurses available and number of patients falling down in hospitals is approximately  r = –0.90. This suggests that hospitals with higher nursing staffing levels tend to have fewer cases of patients falling down.The regression coefficient b is…

An academic aptitude test (X) is used by Enormous University to predict grade-point average (Y) for prospective students. For these two variables, see the data below. Answer this question: predict the grade-point average for a student who has a academic aptitude test score of 22. Screenshot 2026-03-12 at 9.07.29 PM.png

For a normal distribution with mean of 75 and standard deviation of 25, the proportion of the scores between 90 and 100 is…

You are asked to pull two random cards. First, you must pull a King of Hearts out of a 52-card deck.Then, you must pull an Ace of Diamonds out of a different 52 card deck. What is the percent likelihoodof pulling a King of Hearts and an Ace of Diamonds?

Research suggests that people remember uncompleted tasks better than completed ones. It seems that waiters could remember lots of details about customers who did not pay their bills, but they remembered little about those who did.  The X variable is the number of months a bill was outstanding for a customer, and the Y variable was the number of items the waiter could recall about the customer. Screenshot 2026-03-12 at 8.51.33 PM.png Remember to round coefficient a, b, and correlation coefficient (r) to the second decimal place when answering the following questions. A. Calculate r using either formula.      r= B. Find coefficients a and b.      a=           b= C. Provide the unique regression equation for this question. D. Predict the number of months a bill was outstanding for a waiter who remembered 10 items. E. Interpret the meaning of this correlation by filling in the blanks of this sentence. “As ____ (increases/decreases), ______ (increases/decreases).”

Extra credit. If you flip a coin 1000 times and plot the results, what kind of distribution would you have? It’s a Ch7 concept.

                                                   Nurses (X)            Patient Falls (Y)Mean                                            40                        200Standard Deviation                  15                        50Use the data above. Same exact data as the previous question, different question at the bottom. Research has found that the correlation between number of nurses available and number of patients falling down in hospitals is approximately  r = –0.90. This suggests that hospitals with higher nursing staffing levels tend to have fewer cases of patients falling down.For a hospital that employs 60 nurses, how many cases of patients falling down should be expected?