What is the criteria for discarding a data point which you feel may be an untrustworthy outlier?

According to the 68-95-99.7 rule what percent of the population are more than 2 standard deviation away from the mean?

Math SAT Scores (Raw Data, Software Required):
Suppose the national mean SAT score in mathematics is 520. The scores from a random sample of 40 graduates from Stevens High are given in the table below. Use this data to test the claim that the mean SAT score for all Stevens High graduates is the same as the national average. Test this claim at the 0.10 significance level.

AM -vs- PM Height: We want to test the claim that people are taller in the morning than in the evening. Morning height and evening height were measured for 32 randomly selected adults and the difference (morning height) − (evening height) for each adult was recorded. The mean difference was 0.22 cm with a standard deviation of 0.41 cm. Use this information to test the claim that on average people are taller in the morning than in the evening. Test this claim at the 0.01 significance level.

(a) In mathematical notation, the claim is which of the following?

μ > 0μ ≠ 0   
μ < 0μ = 0

(b) What is the test statistic? Round your answer to 2 decimal places.
t_x=

(c) Use software to get the P-value of the test statistic. Round to 4 decimal places.
P-value =

(d) What is the conclusion regarding the null hypothesis?

reject H₀

fail to reject H₀    

(e) Choose the appropriate concluding statement.

The data supports the claim that on average people are taller in the morning than in the evening.

There is not enough data to support the claim that on average people are taller in the morning than in the evening.    

We reject the claim that on average people are taller in the morning than in the evening.

We have proven that on average people are taller in the morning than in the evening.

Gentle Ben is a Morgan horse at a Colorado dude ranch. Over the past 8 weeks, a veterinarian took the following glucose readings from this horse (in mg/100 ml).

The sample mean is x ≈ 94.0. Let x be a random variable representing glucose readings taken from Gentle Ben. We may assume that x has a normal distribution, and we know from past experience that σ = 12.5. The mean glucose level for horses should be μ = 85 mg/100 ml.† Do these data indicate that Gentle Ben has an overall average glucose level higher than 85? Use α = 0.05.

(a) What is the level of significance?


State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test?

H₀: μ = 85; H₁: μ ≠ 85; two-tailed

H₀: μ = 85; H₁: μ > 85; right-tailed  

  H₀: μ = 85; H₁: μ < 85; left-tailed

H₀: μ > 85; H₁: μ = 85; right-tailed

(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.

The Student's t, since we assume that x has a normal distribution with known σ.The standard normal, since we assume that x has a normal distribution with unknown σ.    The standard normal, since we assume that x has a normal distribution with known σ.The Student's t, since n is large with unknown σ.

Compute the z value of the sample test statistic. (Round your answer to two decimal places.)


(c) Find (or estimate) the P-value. (Round your answer to four decimal places.)


Sketch the sampling distribution and show the area corresponding to the P-value.

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?

At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant

.At the α = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.   

At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant

.At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

(e) State your conclusion in the context of the application.

There is sufficient evidence at the 0.05 level to conclude that Gentle Ben's glucose is higher than 85 mg/100 ml.

There is insufficient evidence at the 0.05 level to conclude that Gentle Ben's glucose is higher than 85 mg/100 ml.    

In studies for a​ medication, 10

percent of patients gained weight as a side effect. Suppose 447 patients are randomly selected. Use the normal approximation to the binomial to approximate the probability that

​(a) exactly 45 patients will gain weight as a side effect.

​(b) no more than 45 patients will gain weight as a side effect.

​(c) at least 54 patients will gain weight as a side effect. What does this result​ suggest?

Project: Random variables are all around us, from the time we require to commute to school, to the percentage of lecture material we remember for the exam, we can describe much of the world around us using probability. Project Statement: Find a random variable in your day-to-day life, call it X(ω), and do the following:

• Describe X as either quantitative, qualitative, discrete, continuous, etc.

• Give the support of X (i.e. its possible range of values)

• Speculate on its distribution. Is it normal, geometric, exponential, etc. Give specific reasons and justification for this speculation!

• Sample this random variable at least 5 times. • Use this sample to estimate its parameters.

• Give the newly parameterized distribution explicitly.

A statistical program is recommended.

A certain company produces and sells frozen pizzas to public schools throughout the eastern United States. Using a very aggressive marketing strategy, they have been able to increase their annual revenue by approximately $10 million over the past 10 years. But increased competition has slowed their growth rate in the past few years. The annual revenue, in millions of dollars, for the previous 10 years is shown.

(b)

Using Minitab or Excel, develop a quadratic trend equation that can be used to forecast revenue (in millions of dollars). (Round your numerical values to three decimal places.)

T_t =

(c)

Using the trend equation developed in part (b), forecast revenue (in millions of dollars) in year 11. (Round your answer to two decimal places.)

$  million

• Suppose the possible values of X are {xi}, the possible values of Y are {yj}, and the possible values of X + Y are {zk}. Let Ak denote the set of all pairs of indices (i,j) such that xi+yj =zk;thatisAk ={(i,j):xi+yj =zk}
  a. Argue that

b. Argue that

P{X+Y=zk}= ? P{X=xi,Y=yj} (i,j )∈Ak

E[X+Y]=? ? (xi+yj)P{X=xi,Y =yj} k (i,j )∈Ak

c. Using the formula in b, argue that E[X+Y]=??(xi+yj)P{X=xi,Y =yj}

ij

d. Show that
P(X =xi)=?P(X =xi,Y =yj),P(Y =yj)=?P(X =xi,Y =yj)

ji

e. ProvethatE[X+Y]=E[X]+E[Y]

2. Nine experts rated two brands of Colombian coffee in a taste-testing experiment. A rating on a 7-point scale (1=extremely unpleasing, 7 = extremely pleasing) is given for each of four characteristics: taste, aroma, richness, and acidity. The following data contain the ratings accumulated over all four characteristics:

̅̅̅

1. a) At the 0.05 level of significance, is there evidence of a difference in the mean ratings between the two brands?

2. b) What assumption is necessary about the population distribution in order to perform this test?

3. c) Construct and interpret a 95% confidence interval estimate of the difference in the mean ratings between the two brands.

Instructions:

You must use Excel or a similar statistical software package, such as SPSS, for your assignment.

Tasks:

1.Select thirty stocks (at least 3 different industries) that are listed on the Toronto Stock Exchange.

2.Track each stock’s closing price at the end of the trading day. These closing prices will appear on the Internet. Collect the stock closing price data from January 2017 to December 2019.

4. For each stock, use your data to calculate and interpret: (show calculations)

a)the mean price

b)the median price

c) the standard deviation

d) the range

e) the interquartile range

f)the coefficient of variation

g) 90% confidence interval of mean price using t as the sampling distribution

The USA has an aggregate disposable income of $5.2 trillion and $3.3 trillion in retail sales and a population of 330 million. Small City has an aggregate disposable income of $1.5 billion and $750 million in retail sales and a population of 50 thousand. Mid City has an aggregate disposable income of $5 billion and $2.5 billion in retail sales and a population of 250 thousand. Big City has an aggregate disposable income of $10 billion and $8 billion in retail sales and a population of 600 thousand. What is the BPI for Small City?

Provide a general definition/description of what the estimated standard error of the mean

(SEM) is.

Which of the following conditions must be met to conduct a two-proportion significance test?

1. The populations are independent.
2. The probabilities of success multiplied by the sample sizes are greater than or equal to 10 and the probabilities of failure multiplied by the sample sizes are greater than or equal to 10 for each population.
3. Each sample is a simple random sample.

To investigate the fluid mechanics of swimming, twenty swimmers each swam a specified distance in a water-filled pool and in a pool where the water was thickened with food grade guar gum to create a syrup-like consistency. Velocity, in meters per second, was recorded and the results are given in the table below.

(A) Find the test statistic and P-value. (Round your test statistic to one decimal place and your P-value to three decimal places.)

t=

P-value=