SELECT a simple random sample size 37 from the cereal data. Outline in detail the process you used and identify the fist 4 members of your example.

- Use the variable Mfr for this sample of 37 to answer each of the following.

(a). identify the variable of interest along with the level of measure.

(b) CONSTRUCT a frequency table for the data.

(c) Display the data in a graph. Be sure to include all the proper labels in the graph.

(d) describe the shape of the data if it is appropiate to do so. If it is not appropiate to describe the shape then explain why.

The types of browse favored by deer are shown in the following table. Using binoculars, volunteers observed the feeding habits of a random sample of 320 deer.

Use a 5% level of significance to test the claim that the natural distribution of browse fits the deer feeding pattern.

(a) What is the level of significance?

State the null and alternate hypotheses.

H₀: The distributions are different.

H₁: The distributions are different.

H₀: The distributions are different.

H₁: The distributions are the same.    

H₀: The distributions are the same.

H₁: The distributions are the same.

H₀: The distributions are the same.

H₁: The distributions are different.

(b) Find the value of the chi-square statistic for the sample. (Round the expected frequencies to at least three decimal places. Round the test statistic to three decimal places.)

Are all the expected frequencies greater than 5?

Yes

No    

What sampling distribution will you use?

chi-square

binomial    

normal

uniform

Student's t

What are the degrees of freedom?

(c) Estimate the P-value of the sample test statistic.

P-value > 0.100

0.050 < P-value < 0.100    

0.025 < P-value < 0.050

0.010 < P-value < 0.025

0.005 < P-value < 0.010

P-value < 0.005

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis that the population fits the specified distribution of categories?

Since the P-value > α, we fail to reject the null hypothesis.

Since the P-value > α, we reject the null hypothesis.    

Since the P-value ≤ α, we reject the null hypothesis.

Since the P-value ≤ α, we fail to reject the null hypothesis.

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

At the 5% level of significance, the evidence is sufficient to conclude that the natural distribution of browse does not fit the feeding pattern.

At the 5% level of significance, the evidence is insufficient to conclude that the natural distribution of browse does not fit the feeding pattern

Problem 6.
1. If X N(9; 4), nd Pr(jX ? 2j < 4).
2. If X N(0; 1), nd Pr(jX + 3j > 5).
3. If X N(?2; 9), nd the number c such that Pr(jX + 2j < c) = 0:5.

A device is used in many kinds of systems. Assume that all systems have either 1, 2, 3, or 4 of these devices and that each of these four possibilties is equally likely to be the case. Each device in a system has probablility = 0.1 of failing, and the devices function independently of one another. This implies that once we know how many devices are present, the probability distribution of the number of failures will be known. E.g. if a system employs 3 of the devices, then the number that fail will have a binomial distribution with parameters n = 3 and p = 0.1

Denote with X, the number of failures of devices in the system, and with Y, the total number of devices in the system. What is observed is that for b = 1,2,3, and 4, the conditional probability mass function is the binomial probability mass function with parameters n = b, and p = 0.1

a) Find the joint probability mass table of P(X,Y)

The following random sample of weekly student expenses in dollars is obtained from a normally distributed population of undergraduate students with unknown parameters.

You have been charged to conduct a statistical test in SPSS to verify the claim that the‘average weekly student expenses’ is different than 74 dollars using an alpha level of 5%.

What is the appropriate test that is applicable in this case. Explain your reasoning.

State the null and alternate hypotheses in this case using proper statistical notations.

List one assumption that you are making about the distribution.

Insert a copy of the summary table of descriptive statistics generated in SPSS.

Insert a copy of the table for the statistical test you conducted in SPSS.

Drawing on information from the tables in (e) and/or (f) show how they relate to t-statistic as obtained in SPSS.

What is/are the critical value(s) of the test statistic at the 5% significance level.

What can you conclude about the claim based on the results generated from the statistical test? Make sure to support your conclusion by referencing the appropriate statistics from the test.

Compute the 90% confidence interval for the average weekly expenses.

Compute the Cohen’s d effect size.

​It's tough to find out how much people​ earn, but in​ 2011, a magazine reported that the average​ lawyer's salary in a country was $64,000. Suppose that today you interview a random sample of 55 lawyers in the country and find that the average salary is $75,275​, with a standard deviation of $82,694.Do you think the average​ lawyer's salary today is higher than that reported by the magazine in​ 2011? For this​ problem, assume alphaαequals=0.05.

Let muμ be the population mean​ lawyer's salary in the country.

Determine the null and alternative hypotheses.

H0 : u = 64,000

HA : u > 64,000

Test statistic is 1.01

What is the P-Value?

Suppose a 90% confidence interval for the mean salary of college graduates in a town in Mississippi is given by [$45,783, $57,017]. The population standard deviation used for the analysis is known to be $13,700. [You may find it useful to reference the z table.]

a. What is the point estimate of the mean salary for all college graduates in this town?

b. Determine the sample size used for the analysis. (Round "z" value to 3 decimal places and final answer to the nearest whole number.)

You read in the results section of an article in a psychology journal that the results of at-test for independent sample means revealed a significant t12 = 1.8, with σˆX1−X2 = 2. If there were 8 participants in the experimental group,

(a) how many participants were in the corresponding control group?

(b) what significance level was used, and was the test a one-tailed or a two-tailed test?

(c) what was the mean difference between the experimental and the control groups?

The length of time for an individual to wait at a lunch counter is a random variable whose density function is

f(x) = (1/4)e^(-x/4) for x > 0 and = 0 otherwise

a) Find the mean and the variance

b) Find the probability that the random variable is within three standard deviations of the mean and compare Chebyshev's Theorem.

Solve for x -2 < (1/6)(10-x) < 2

Problem 8-12 (Algorithmic)

Many forecasting models use parameters that are estimated using nonlinear optimization. The basic exponential smoothing model for forecasting sales is

F_{t + 1} = αY_t + (1 – α)F_t

where

This model is used recursively; the forecast for time period t + 1 is based on the forecast for period t, F_t; the observed value of sales in period t, Y_t and the smoothing parameter α. The use of this model to forecast sales for 12 months is illustrated in the table below with the smoothing constant α = 0.3. The forecast errors, Y_t - F_t, are calculated in the fourth column. The value of α is often chosen by minimizing the sum of squared forecast errors, commonly referred to as the mean squared error (MSE). The last column of Table shows the square of the forecast error and the sum of squared forecast errors.

In using exponential smoothing models, we try to choose the value of α that provides the best forecasts. Build an Excel Solver or LINGO optimization model that will find the smoothing parameter, α, that minimizes the sum of squared forecast errors. You may find it easiest to put table into an Excel spreadsheet and then use Solver to find the optimal value of α. If required, round your answer for α to three decimal places and the answer for the resulting sum of squared errors to two decimal places.

The optimal value of α is  and the resulting sum of squared errors is .

A university would like to examine the linear relationship between a faculty​ member's performance rating​ (measured on a scale of​ 1-20) and his or her annual salary increase. The table to the right shows these data for eight randomly selected faculty members. Complete parts a and b. Rating Increase 16 2300 18 2400 12 1800 12 1600 16 2000 14 2700 18 1900 17 1800

Let x be a random variable that represents the percentage of successful free throws a professional basketball player makes in a season. Let y be a random variable that represents the percentage of successful field goals a professional basketball player makes in a season. A random sample of n = 6 professional basketball players gave the following information.

(c) Verify that S_e ≈ 3.0468, a ≈ 8.188, b ≈ 0.5168, and x ≈ 73.167.

(e) Find a 90% confidence interval for y when x = 83. (Round your answers to one decimal place.)

(f) Use a 5% level of significance to test the claim that β > 0. (Round your answers to two decimal places.)

Ch. 11, 2. Given two dependent random samples with the following results:

Can it be concluded, from this data, that there is a significant difference between the two population means?

Let d= (Population 1 entry)−(Population 2 entry)d=(Population 1 entry)−(Population 2 entry). Use a significance level of α=0.2 for the test. Assume that both populations are normally distributed.

Step 1 of 5: State the null and alternative hypotheses for the test.

Ho: μd(=,≠,<,>,≤,≥) 0

Ha:μd (=,≠,<,>,≤,≥) 0

Step 2 of 5: Find the value of the standard deviation of the paired differences. Round your answer to one decimal place.

Step 3 of 5: Compute the value of the test statistic. Round your answer to three decimal places.

Step 4 of 5: Determine the decision rule for rejecting the null hypothesis H0. Round the numerical portion of your answer to three decimal places.

Reject Ho if (t, I t I) (<,>) _____

Step 5 of 5:

Make the decision for the hypothesis testTop of Form

Reject Null Hypothesis Fail to Reject Null Hypothesis