Suppose you are a rabid football fan and you get into a discussion about the importance of offense (yards made) versus defense (yards allowed) in terms of winning a game. You decide to look at football statistics to provide evidence of which variable is a stronger predictor of wins.

Can use the minitab. Part a) Develop a simple linear regression that compares wins to yards made (please show me the scatter plot) . Perform the following diagnostics on this regression: 1) test of significance on the slope; 2) assess the fit of the line using the appropriate statistics; 3) interpret the slope of the equation if the slope is significant. Part b) Develop a simple linear regression that compares wins against yards allowed. Perform the following diagnostics on this regression: 1) test of significance on the slope; 2) assess the fit of the line using the appropriate statistics; 3) interpret the slope of the equation if the slope is significant. Part c) Which explanatory variable provides a better prediction of the response variable? Support your answer briefly by citing the appropriate diagnostics. Note: Use an alpha of .05 for both tests of significance. Be sure to show ALL steps of the hypothesis testing procedure

EXCEL DATA TO USE.

1/ Assume that the readings at freezing on a batch of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A single thermometer is randomly selected and tested. Find P₃₁, the 31-percentile. This is the temperature reading separating the bottom 31% from the top 69%.
P₃₁ = °C
(Round answer to three decimal places)

2/ Engineers must consider the breadths of male heads when designing helmets. The company researchers have determined that the population of potential clientele have head breadths that are normally distributed with a mean of 6.9-in and a standard deviation of 1.2-in. Due to financial constraints, the helmets will be designed to fit all men except those with head breadths that are in the smallest 1.7% or largest 1.7%.
What is the minimum head breadth that will fit the clientele?
min =
What is the maximum head breadth that will fit the clientele?
min =
Enter your answer as a number accurate to 1 decimal place. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

3/ The amounts of nicotine in a certain brand of cigarette are normally distributed with a mean of 0.958 g and a standard deviation of 0.322 g. Find the probability of randomly selecting a cigarette with 0.314 g of nicotine or less.
P(X < 0.314 g) =
Enter your answer as a number accurate to 4 decimal places. NOTE: Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

4/ In the country of United States of Heightlandia, the height measurements of ten-year-old children are approximately normally distributed with a mean of 56.5 inches, and standard deviation of 7 inches.
What is the probability that the height of a randomly chosen child is between 55.4 and 68.2 inches? Do not round until you get your your final answer, and then round to 3 decimal places.
Answer= (Round your answer to 3 decimal places.)

5/ A manufacturer knows that their items have a normally distributed lifespan, with a mean of 6.9 years, and standard deviation of 2.1 years.
If you randomly purchase one item, what is the probability it will last longer than 4 years?
Round answer to three decimal places

Question

Directions: Answer the questions about the story.

Summarize the story using your own words.

What kind of personality do you think Ken has based on the story?

Is there evidence that the mean annual salary of a Tesla owner is more than $253500? Data was collected from 36 Tesla owners across the US. The mean annual salary of those 36 Tesla owners was $254000 with a standard deviation of $1057.  Answer this question,  at the 1% significance level, by performing the following steps of a hypothesis test .

a) Complete the null and alternative hypotheses by typing into the box as indicated.

Ho : mu   (Type one:  <, =, >)    (type a value)
Ha : mu   (Type one:  <, =, >)    (type a value)

b)  Complete the probability statement for the probability of observing a mean salary at least as extreme as the one measured for this sample.

P( X_bar __(I)__ __(II)__ )

• Which symbol goes in blank (I)? Choose one:  <, =, >. Type the answer into this box.
• What number goes in blank (II)? Type the relevant number into this box.

c)  Complete the following sentence. For each box, choose an option and type its corresponding letter (A, B, etc...) into the box .

This test uses the  (A.  z B. t  C.  F) test statistic. Calculating this test statistic requires knowing the standard deviation of the  (A.  sample B.  population).

d) Calculate the test statistic. Type the value, rounded to 2 decimals, in the box.

Answer for (d):  

e) This figure represents the density curve of the test statistic. Answer the questions below about the distribution.

• What is the value of the test statistic at the center of the distribution? Type the number in the box.
  
  Answer:  
  
• Which shaded region or regions best represent the P-value for this test?   Choose an option from the list and type its letter (A, B, or C) in the box
  
  A. I B. II  C I and II
  
  Answer:  
  
• How many degrees of freedom are there for this distribution? Type the number in the box.
  
  Answer:   

f) Find an interval containing this test's P-value using one of the following tables:  normal table, t-table.  Type values for the lower and upper bounds, recorded to 4 decimals, into the correct boxes.

Answer for (f):   P-Value

g) Complete this concluding sentence. For each box, choose one of the two options and type its corresponding letter (A or B) into the box.

We  (A.  reject  B.  fail to reject) the null hypothesis. There (A.  is  B.  is no) evidence that the mean annual salary of a Tesla owner is (A.  less  B.  more) than $253500 at the 1% significance level. This refers to the (A.  sample  B.  population).

A supermarket you work part-time at has one express lane open from 5 to 6 PM on weekdays (Monday through Friday). This time of the day is usually the busiest since people tend to stop on their way home from work to buy groceries. The number of items allowed in the express lane is limited to 10 so that the average time to process an order is fairly constant at about 1 minute. The manager of the supermarket notices that there is frequently a long line of people waiting and hears customers grumbling about the wait. To improve the situation he decides to open additional express lanes during this time period. If he does, however, he will have to "pull" workers from other jobs around the store to serve as cashiers. Hence, he is reluctant to open more lanes than necessary.
Knowing that you are a college student studying probability, your manager asks you to help him decide how many express lanes to open. His requirement is that there should be no more than one person waiting in line 95% of the time.
With the task at hand, you set out to study the problem first. You start by counting the number of customer arrival in the express lane on a Monday from 5 to 6pm. There are a total of 81 arrivals. You repeat the experiment on the following four days (Tuesday through Friday) and note the total arrivals of 68, 72, 61 and 66 customers, respectively.

1) What is the average number of customer arrivals at the express lane from 5 to 6pm on weekdays?

2) Assume the customer arrivals at the express lane from 5 to 6pm on weekdays can be modeled by a Poisson random variable, what is the PMF for the number of customers arrived during a one-minute interval in this period?

3) What is the probability of two or fewer customers arriving at the one express lane during a oneminute interval in this period? Does it satisfy the manager’s requirement of no more than one person waiting in line 95% of the time?

4) If your answer to the previous question is no, how many express lanes should the manager open in order to satisfy his requirement? You can assume that the arriving customer is equally likely to join any of the express lane if there are more than one express lanes. Also you can assume the lanes are independent, but all lanes must satisfy the manager’s requirement.

Isabel Briggs Myers was a pioneer in the study of personality types. The personality types are broadly defined according to four main preferences. Do married couples choose similar or different personality types in their mates? The following data give an indication. Similarities and Differences in a Random Sample of 375 Married Couples Number of Similar Preferences Number of Married Couples All four 27 Three 124 Two 118 One 70 None 36 Suppose that a married couple is selected at random.

1(a) Use the data to estimate the probability that they will have 0, 1, 2, 3, or 4 personality preferences in common. (For each answer, enter a number. Enter your answers to 2 decimal places.) 0=____ 1=____   2=_____ 3=_____ 4=________

1(b) Do the probabilities add up to 1? Why should they?

a. Yes, because they do not cover the entire sample space.

b. No, because they do not cover the entire sample space.

c. Yes, because they cover the entire sample space.

d. No, because they cover the entire sample space.

What is the sample space in this problem?

a. 0, 1, 2, 3 personality preferences in common

b. 1, 2, 3, 4 personality preferences in common

c. 0, 1, 2, 3, 4, 5 personality preferences in common

d. 0, 1, 2, 3, 4 personality preferences in common

2. Consider the data set.

• 2, 3, 4, 5, 6

(a)

Find the range. (Enter an exact number.)=______

(b)

Use the defining formula to compute the sample standard deviation s. (Enter a number. Round your answer to two decimal places.)=______

(c)

Use the defining formula to compute the population standard deviation σ. (Enter a number. Round your answer to two decimal places.)=____

Consider the probability that no less than 88 out of 158 computers will not crash in a day. Assume the probability that a given computer will not crash in a day is 57%.

Approximate the probability using the normal distribution. Round your answer to four decimal places.

A digital chip contains 100 transistors and 400 connections. The probability of a faulty transistor is 10^-3 and the probability of faulty connection is 10^-4. What is the probability that a given chip taken at random is defective, assuming all defects are independent?​

(a) What is the probability that a 5-card poker hand has at least three spades?

(b)What upper bound does Markov’s Theorem give for this probability?

(c)What upper bound does Chebyshev’s Theorem give for this probability?

(a) What is the probability that a 5-card poker hand has at least three spades?

(b) What upper bound does Markov’s Theorem give for this probability?

(c) What upper bound does Chebyshev’s Theorem give for this probability?