Statistics and Probability Answers

Let T be a random variable giving the number of heads plus the number of tails in three tosses of a coin. List the elements of the sample space S for the three tosses of the coin and assign a value to each sample point.

An emergency service wishes to determine whether a relationship exists between the outside temperature and the number of emergency calls it receives for a 7-hour period. The data are shown. (25 points)
Temperature x 25 10 27 30 33
No. of calls y 7 4 8 10 11

a) Find the correlation coefficient r (If you use any software or online calculator, please take the screenshot.


b) Find the regression equation (If you use any software or online calculator, please take the screenshot. You will get extra points if you do by hand.)


c) Graph the regression equation. (If you use any software or online calculator, please take the screenshot.

Consider a pair of ten sided dice. (a) what is the probability of rolling nines for both dice. (b) what is the probability that the sum of the dice is 18?

1.1 A college professor randomly selects 25 freshman to study the mathematical background of the incoming freshman class. The average SAT score of these 25 students is 565 and the standard deviation is estimated to be 40. Using the information, can the professor theft the null hypothesis that the average test score is 550 or less?
Use a 5% level of significance

1.2 suppose the college professor in question 1.1 wants to know whether the mathematical aptitude of freshman has improved over the past year. He randomly draws the 25 SAT Mathematics scores from last year's freshman class and obtains a sample mean of 560 and a sample standard deviation of 35. Compare the results from last year with the results from this year. Do the data offer enough evidence for rejecting the null hypothesis that there is no improvement?
Use a 5% level of significance

Forty-four percent of US adults have little confidence in their cars. You randomly select twelve US adults. Find the probability that the number of US adults who have little confidence in their cars is (1) exactly six and then find the probability that it is (2) more than 7.

the life of a 60-watt light bulb in hours is known to be normally distributed with a 25 hours. create 5 different random samples of 100 bulbs each which has a mean life of x bar 1000 hours and perform one-way anova with state it. Please solve using Excel and explain it clearly

A planning committee for a project must consist of six members. There are 8 architects and 5 engineers. In how many different ways can this planning committee be formed?

Ramos is concerned about the number of prescriptions his elderly clients have. He would like to create a 99% confidence interval for the mean number of prescriptions per client with a maximum error of 2 prescriptions. Assuming a standard deviation of 5.2 prescriptions, what is the minimum number of clients he must sample?

In “The Probable Error of a Mean” by William Gosset (Biometrika, Vol. VI, No.1) published in 1908,
the following values were listed for the yields of head corn in pounds per acre. These values resulted
from using seeds that were kiln-dried.
2009,1915,2011,2463,2180,1925,2122,1482,1542,1443,1535
Assuming measurements are normally distributed, test that the population mean is different from 2020.
(a) What is the absolute test statistic? Blank 1. Fill in the blank, read surrounding text.

(b) What is the p-value?