The weights​ (in pounds) of 6 vehicles and the variability of their braking distances​ (in feet) when stopping on a dry surface are shown in the table. Can you conclude that there is a significant linear correlation between vehicle weight and variability in braking distance on a dry​ surface? Use alphaequals0.01. ​Weight, x 5930 5350 6500 5100 5870 4800 Variability in braking​ distance, y 1.71 1.95 1.93 1.65 1.68 1.50

A study found that highway drivers in one state traveled at an average speed of 59.7 miles per hour​ (MPH). Assume the population standard deviation is 6. MPH. Complete parts a through d below.

a. What is the probability that a sample of 30 of the drivers will have a sample mean less than 58 ​MPH? (Round to four decimal places as​ needed.)

b. What is the probability that a sample of 45 of the drivers will have a sample mean less than 58 ​MPH? (Round to four decimal places as​ needed.)

c. What is the probability that a sample of 60 of the drivers will have a sample mean less than 58​ MPH? (Round to four decimal places as​ needed.)

d. Explain the difference in these probabilities. (Select one each) As the sample size​ increases, the standard error of the mean (Same, Increase, Decrease) As the sample size​ increases, the standard error of the mean (Same, Move farther, Move closer) the population mean of 59.7 MPH.​ Therefore, the probability of observing a sample mean less than 58 MPH (Same, Increase, Decrease).

Suppose you select a card at random from a standard deck, and then without putting it back, you select a second card at random from the remaining 51 cards. What is the probability that both cards have the same rank, or both have the same suit, or one is red and one is black?

Dose the scatter plot show a trend? If so, what is the trend?

If there is a trend in the data, how many sales would you expect if the temperature outside is 90 degrees?

Group of answer choices

500

None of these

750

There is no trend.

250

Suppose we have the following facts about customers at a supermarket:

60% buy bread (B).

55% buy milk (M).

45% buy eggs (E).

78% buy bread or eggs.

38% buy bread and milk.

30% buy milk and eggs.

19% buy all three items.

. If we randomly select a customer, what is the probability the customer buys none of the

three items?

(A) 0.12

(B) 0.13

(C) 0.14

(D) 0.15

(E) 0.16

Assume that X is a random variable with density corresponding to an equal mixture of two Gaussians, with unknown means µ1, µ2 and unknown variances σ1, σ2: p(x) = 0.5N (µ1, σ2 1 ) + 0.5N (µ2, σ2 2 ).

(1) Assume you are given a dataset of n iid samples from this distribution: D = {xi} n i=1. Your goal is to estimate µ1, µ2, σ1 and σ2.

(a) [10 marks] Write down the negative log-likelihood for this problem, for the given dataset D = {xi} n i=1. Simplify as far as you can, by explicitly writing the densities for a Gaussian. Hint: You will not be able to simplify very far, and you will be stuck with a few exponentials that the logs cannot cancel.

(b) [10 marks] Derive update rules to estimate µ1, µ2, σ1, and σ2. More specifically, derive the gradient descent update rule, for the negative log likelihood you provided above.

Find the cash value of the lottery jackpots given below. Yearly jackpot payments begin immediately. Assume the lottery can invest at the given interest rates.

(round to nearest dollar amount)

15-6: Consider the following set of data:

x₁              10        8          11        7          10        11            6

x₂         50        45        37        32        44        51            42

y          103      85        115      73        97        102            65

1. Obtain the estimate regression equation.

2. Examine the coefficient of determination and the adjusted of determination. Does it seem that either of the independent variables’ addition to R² does not justify the reduction in degrees of freedom that results from its addition to the regression model? Support your assertions.

3. Conduct a hypothesis test to determine if the dependent variable increases when x₂ increases. Use a significance level of 0.025 and the p-value approach.

4. Construct a 95% confidence interval for the coefficient of x_1.

Suppose X is a uniform random variable on the interval (0, 1). Find the range and the distribution and density functions of Y = Xn for n ≥ 2.

A recent survey conducted by a foundation reported that 74​% of teens admitted to texting while driving. A random sample of 42 teens is selected. Use the normal approximation to the binomial distribution to answer parts a through e.

a. Calculate the mean and standard deviation for this distribution.

The mean is _________.

​(Round to four decimal places as​ needed.)

The standard deviation is ___________.

b. What is the probability that more than 36 of the 42 teens admit to texting while​ driving?

The probability is __________..

​(Round to four decimal places as​ needed.)

c. What is the probability that exactly 24 of the 42 teens admit to texting while​ driving?

The probability is _____________.

​(Round to four decimal places as​ needed.)

d. What is the probability that 27​, 28​, or 29 of the 42 teens admit to texting while​ driving?

The probability is ___________.

​(Round to four decimal places as​ needed.)

e. What is the probability that fewer than 32 of the 42

teens admit to texting while​ driving?

The probability is ___________.

​(Round to four decimal places as​ needed.)

A retailer discovers that 3 jars from his last shipment of Spiffy peanut butter contained between 15.85 and 15.92 oz of peanut butter, despite the labeling indicating that each jar should contain 16 oz. of peanut butter. He is wondering if Spiffy is cheating its customers by filling its jars with less product than advertised. He decides to measure the weight of 50 jars from the shipment and use hypothesis testing to verify this.

1. (f) In his sample of 50 jars, the retailer finds an average weight of 15.84 oz and a sample standard deviation of 0.5 oz. He decides to use a significance level of 0.04. What is the conclusion from this hypothesis testing? Can you conclude that Spiffy is cheating its customers?

2. (g) What is the p-value? What is the meaning of this number?

3. (h) For what values of the sample mean would the null hypothesis be rejected?

4. (i) Calculate the probability of type II error if the true mean is 15.7 oz.

5. (j) Solve (f), (h) and (i) when the level of significance is 0.01. Is your new answer for (f) consistent with the p-value found in (g)? How is the probability of type II error affected when the probability of type I error changes?

MT scores: 11, 11, 16, 17, 19, 20, 21, 21 23 24 24 26 26 27 27 28 28 28 29 30 31 31 32 33 35 37 38 38 39 42 44

Questions for Class MT Score Distribution Analysis

1. Create a histogram of MT scores.

2. Describe the shape of the MT scores distribution.

3. Compute the mean and standard deviation.

4. Compute the 5-number summary.

5. Create a boxplot of MT scores.

6. Compute the probability that a randomly selected student from the class scored higher than 20.

7. Are the MT scores normally distributed? Why or why not?

8. Assuming a normal fit, compute the percentile of your score.

9. Compute your actual percentile from the raw data.

10. Do your computations for #8 and 9 support your answer to #7? Why or why not?

In this lab we will test to see if there is evidence of a difference in the average age for at least 1 of 4 groups

of marital status (i.e., single, married, divorced, widowed). Use ?= 0.05.

To include in your submission:

ü Copy the ANOVA Table from the SPSS output to your Word document. Please make sure to adjust the

size of your tables so that they fit on the page.

ü Using the ANOVA table, answer the following for the one-way ANOVA:

a. Type the hypotheses.

b. Type in the test statistic found from the SPSS output.

c. Type in the p-value found from the SPSS output.

d. Type your decision regarding the null hypothesis.

e. Type in your conclusion using context and units from the problem

1. The weights of newborn children in the U.S. vary according to the normal distribution with mean 7.5 pounds and standard deviation 1.25 pounds. The government classifies a newborn as having low birth weight if the weight is less than 5.5 pounds.       

a) You choose 3 babies at random. What is the probability that their average birth weight is less than 5.5 pounds?

b) What is the third quartile of the distribution?

Regular gasoline averaged ​$2.83 per gallon in December 2018. Assume the standard deviation for gasoline prices is ​$0.14 per gallon. A random sample of 40 service stations was selected. Complete parts a through d.

a. What is the probability that the sample mean will be less than ​$2.84?

The probability that the sample mean will be less than $2.84 is ______

​(Type an integer or decimal rounded to four decimal places as​ needed.)

b. What is the probability that the sample mean will be more than ​$2.87?

The probability that the sample mean will be more than ​$2.87 is ________.

​(Type an integer or decimal rounded to four decimal places as​ needed.)

c. What is the probability that the sample mean will be between $2.81 and $2.91​?

The probability that the sample mean will be between $2.81 and ​$2.91 is _________.

​(Type an integer or decimal rounded to four decimal places as​ needed.)

d. Suppose the sample mean is $2.89. Does this result support the average gasoline price​ findings? Explain your answer.

The probability that the average price per gallon is more than ​$2.89 is ________.

​(Type an integer or decimal rounded to four decimal places as​ needed.)

Does this result support the average gasoline price findings? Explain your answer. Consider a probability of less than 0.05 to be small.

A) The probability supports the finding that the average price per gallon for gas in the population is ​$2.83​, because this probability is small.

B) The probability does not support the finding that the average price per gallon for gas in the population is ​$2.83​, because this probability is large. "

C)The probability supports the finding that the average price per gallon for gas in the population is ​$2.83, because this probability is large.

D)The probability does not support the finding that the average price per gallon for gas in the population is ​$2.83​, because this probability is small.