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

A poll printed the results of a survey of 880Americans focusing on their perception of the quality of Japanese products. It has been observed that the sentiment towards Japanese products has actually improved over time. Is there sufficient evidence to conclude that American sentiment towards Japanese products changed from 1999 to 2005?

Step 8 of 10 :  Find the critical value of the test at the 0.05 level of significance. Round your answer to three decimal places.

Step 9 of 10: Make the decision to reject or fail to reject the null hypothesis at the 0.05 level of significance.

Step 10 of 10: State the conclusion of the hypothesis test at the 0.05 level of significance.

A researcher obtained the ordinary least squares (OLS) estimates for a Ghanaian firm's stock price using 120 observations from 1980 ml to 1989 m 12 (All variables in logarithms) as:

In S_t = 0.87 -054 In p_t + 0.65 In y_t + 0.34 In r_t - 0.32 In m_t

Standard errors:

p_t = (1.06)

y_t = (0.24)

r_t = (0.12)

m_t = (0.24)

Adjusted R²=0.34, RSS = 1.24, F₁₁₅⁴ =3.75

S_t are the log of the stock price, p_t is the log of profit, y_t is the log of its output in Ghana, r_t is the log of expenditure on research and development and m_t is the log of expenditure on marketing. Figures in parentheses are standard errors and RSS is the Residual Sum of squares.

Required:

(a) Interpret fully the regression results.

(b) Briefly evaluate the reasons behind including p_t and y_t as explanatory variables in the regression

(c) What is the explanatory power of the regression?

(d) Test, whether each coefficient equals 0, at the 5% level of significance

(e) Using a t-test, does the coefficient on the variable In y_t = 1?

(f) What are the policy implication of the result

Meteorites randomly strike the earth’s surface at an average rate of 90 meteorites per hour.

(a) Find the probability that at least 4 meteorites strike the earth during a three-minute interval.

(b) Find the probability that the time between two consecutive meteorites striking the earth is greater than 20 seconds. Derive the formulation using the c.d.f., but do not calculate it.

(c) Find the probability that the time until 4 meteorites strike the earth is greater than 2 minutes.

(d) Calculate the expected time until 4 meteorites strike the earth.

I know we use poissons distribution but im having trouble breaking down and understanding this problem.

40 numbers are rounded off to the nearest integer and then summed. If the individual round-off error are uniformly distributed over (−.5,.5) what is the probability that the resultant sum differs from the exact sum by more than 2 ?