1.

You manage a local tex-mex restaurant called “Garage Taco Bar.” You have recently switched all of your business to takeout due to the pandemic and you want to make sure you are still making enough money to stay open. The owner says that to keep everything running you need to be making more than $3,000 per day in takeout orders. Looking back on your records you take a random sample of 8 days and determine the following sample statistics. Assume the daily revenue is approximately normal.

Garage Taco Bar daily revenue: x1=$3,103, s1=$154

You decide you should run a hypothesis test to determine if you should stay open.

a. Define the hypotheses for this test. Is this a one-tailed or two-tailed test? If one-tailed, is it upper- or lower-tailed?

b. Give a rejection region for this test based on an α=0.05 significance level.

c. Solve for the test statistic and interpret the results of the test.

2. One of your workers has a friend at a competing restaurant “Dos Rios,” and they tell you that they have also thought about closing. You find that Dos Rios has also randomly sampled days to estimate their daily revenue. Your worker’s friend gives you the following statistics based on 10 randomly sampled days. Assume the distribution is approximately normally distributed, and that the true variance is equal to that of “Garage”.

Dos Rios daily revenue: x2= $2,791 S2= $151

You go to the owner with this information, and they tell you that knowing this, “Garage Taco Bar” should stay open if they are making significantly more money per day than Dos Rios.

You decide you need to run a new hypothesis test.

a. Define the parameter of interest in this test, and calculate the point estimate.

b. Find a rejection region for this test based an α=0.05 significance level and calculate the test statistic.

c. Interpret the results of the test.

Discuss how the concept of statistical independence underlies statistical hypothesis testing in general. Based on statistical analysis, are we justified in asserting that two variables are statistically dependent? Why or why not? Explain why researchers typically focus on statistical independence rather than statistical dependence.

A random sample of 89 tourist in the Chattanooga showed that they spent an average of $2,860 (in a week) with a standard deviation of $126; and a sample of 64 tourists in Orlando showed that they spent an average of $2,935 (in a week) with a standard deviation of $138. We are interested in determining if there is any significant difference between the average expenditures of those who visited the two cities? a) Determine the degrees of freedom for this test. b) Compute the test statistic c) Compute the p-value(please show working of calculation) d) What is your conclusion?

You manage a local tex-mex restaurant called “Garage Taco Bar.” You have recently switched all of your business to takeout due to the pandemic and you want to make sure you are still making enough money to stay open. The owner says that to keep everything running you need to be making more than $3,000 per day in takeout orders. Looking back on your records you take a random sample of 8 days and determine the following sample statistics. Assume the daily revenue is approximately normal.

Garage Taco Bar daily revenue: x1=$3,103, s1=$154

You decide you should run a hypothesis test to determine if you should stay open.

a. Define the hypotheses for this test. Is this a one-tailed or two-tailed test? If one-tailed, is it upper- or lower-tailed?

b. Give a rejection region for this test based on an α=0.05 significance level.

c. Solve for the test statistic and interpret the results of the test.

Use technology to find the​ P-value for the hypothesis test described below. The claim is that for a smartphone​ carrier's data speeds at​ airports, the mean is muμequals=19.0019.00 Mbps. The sample size is nequals=2222 and the test statistic is tequals=1.7981.798. ​P-valueequals=nothing ​(Round to three decimal places as​ needed.)

Suppose that the failure rate (failing to detect smoke when smoke is present) for a brand of smoke detector is 1 in 2000. For safety, two of these smoke detector are

installed in a laboratory.

(a) What is the probability that smoke is not detected in the laboratory when smoke

is present in the laboratory?

(b) What is probability that both detectors sound an alarm when smoke is present in

the laboratory?

(c) What is the probability that one of the detectors sounds the alarm and the other

fails to sound the alarm when smoke is present in the laboratory?

Probability and Statistics

Could you please solve the following questions with specifying the answers

A. What is the probability that z, the standard normal distribution, is less than 1.75 standard deviations below the mean of zero?

a. 5%      b. 4%      c. 6%      d. 7.4%

B. If two random samples of the heights of adult males in New York are taken, one of 400, the other of 900 people, which one would likely have the larger range from shortest to tallest?

a. the 400 person sample      b. the 900 person sample    c. they’d be equal

C. The p-value of a test of the null hypothesis is 3.5%. This means

a. the hypothesis is true with probability 3.5% or possibly less than 3.5%

b. the alternative hypothesis is true with probability 3.5% or possibly less

c. 3.5% is the probability of finding the observed or more extreme results when the null hypothesis (H ₀) is true

d. None of the above

D. One of the main reasons to be interested in the regression line of y on x is that

a. one can use it to predict y-values from different x-values

b. one can determine the standard deviation of y     

c. one can determine from it the values of the quartiles of x and y.

The Table below shows data of two random samples of employee wages taken from two small business firms providing the same service. The issue to be evaluated is whether the average wage in these two firms is the same. Test this hypothesis at α = 0.05.

Values of Test-Statistics, zo, critical statistic are ?? and the decision is to ....

Wages from two small business firms

Determine the mean and standard deviation of your sample.

Find the 80%, 95%, and 99% confidence intervals. Make sure to list the margin of error for the 80%, 95%, and 99% confidence interval.

Create your own confidence interval (you cannot use 80%, 95%, and 99%) and make sure to show your work.

Make sure to list the margin of error.

What trend do you see takes place to the confidence interval as the confidence level rises?

Explain mathematically why that takes place.

Provide a sentence for each confidence interval created in part c) which explains what the confidence interval means in context of topic of your project. Explain how Part I of the project has helped you understand confidence intervals better? How did this project help you understand statistics better?

Answer using data below. These are the points made in the first 50 games of a NBA basketball team.

120, 124, 113, 97, 127, 96, 100, 121, 115, 109, 114, 109, 116, 110, 132, 104, 111, 104, 101, 107, 98, 135, 105, 109, 121, 107, 118, 109, 145, 98, 136, 117, 103, 118 126 129 121 105 100 120 107 120 121 99 106 109 127 114 105 102 I need all questions answered please!

Consider the following hypotheses:

H₀: μ = 380
H_A: μ ≠ 380

The population is normally distributed with a population standard deviation of 77. (You may find it useful to reference the appropriate table: z table or t table)

a-1. Calculate the value of the test statistic with x−x− = 390 and n = 45. (Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.)

a-2. What is the conclusion at the 10% significance level?

• Reject H₀ since the p-value is less than the significance level.

• Reject H₀ since the p-value is greater than the significance level.

• Do not reject H₀ since the p-value is less than the significance level.

• Do not reject H₀ since the p-value is greater than the significance level.

a-3. Interpret the results at αα = 0.10.

• We conclude that the population mean differs from 380.

• We cannot conclude that the population mean differs from 380.

• We conclude that the sample mean differs from 380.

• We cannot conclude that the sample mean differs from 380.

b-1. Calculate the value of the test statistic with x−x− = 345 and n = 45. (Negative value should be indicated by a minus sign. Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.)

b-2. What is the conclusion at the 5% significance level?

• Reject H₀ since the p-value is greater than the significance level.

• Reject H₀ since the p-value is less than the significance level.

• Do not reject H₀ since the p-value is greater than the significance level.

• Do not reject H₀ since the p-value is less than the significance level.

b-3. Interpret the results at αα = 0.05.

• We conclude that the population mean differs from 380.

• We cannot conclude that the population mean differs from 380.

• We conclude that the sample mean differs from 380.

• We cannot conclude that the sample mean differs from 380.

Probability and Statistics

Could you please solve the following questions with specifying the answers

A. When finding confidence intervals, the interval is smaller if

a.sample size and standard deviation are bigger

b.sample size and standard deviation are smaller

c.sample size is bigger, but the standard deviation is smaller

d.sample size is smaller, but standard deviation is bigger.    

B. If the birth weights of the babies born annually in a hospital is Normal with a mean of 5 pounds 10 ounces and a standard deviation of 5 ounces, what percentage of babies are born weighing less than 5 pounds? (No table needed.)

a. 13.5%       b. 2.5%       c. 16%        d. .3%

C. What percent of the babies born weigh between 5 pounds and 5 pound 5 ounces? (Again no table.)

a. 13.5%       b. 47.5%       c. 16%        d. 34%

D. Of the 40 babies born during the first weeks of next month, how many are likely to be under five pounds?

a. 4      b. 2      c. 6     d. 1     

A real estate agent in Athens used regression analysis to investigate the relationship between apartment sales prices and the various characteristics of apartments and buildings. The variables collected from a random sample of 25 compartments are as follows:
Sale price: The sale price of the apartment (in €)
Apartments: Number of apartments in the building
Age: Age of the building (in years)
Size: Apartment size (area in square meters)
Parking spaces: Number of car parking spaces in the building
Excellent building condition (Pseudo-variable): 1 if the condition of the building is
excellent, 0 different
Good building condition (Pseudo-variable): 1 if the condition of the building is
good, 0 different

We have the following results of regression analysis with the OLS method:

Questions:
1. State the estimated regression equation.

2. Comment on the importance of the regression rates.

3. Give the interpretation of the regression coefficients.

Mark all pairs of H₀/H₁ below as valid (V) or invalid (I):

1. H₀: p = 0.4 vs.   H₁: p > 0.4
2. H₀: p ≠ 0.53 vs.   H₁: p = 0.53
3. H₀: σ² = 15 vs.   H₁: σ² ≠ 15
4. H₀: µ = 3   vs.   H₁: σ² ≠ 9
5. H₀: µ = 4   vs.   H₁: µ ≠ 0.2

In a survey, 600 consumers were asked whether they would like to purchase a domestic or a foreign made automobile. 340 said that they preferred to purchase a domestic made automobile. Construct and explain a 95% confidence interval estimate for the proportion of all consumers who prefer domestic automobiles.

1. Twenty male athletes were given a special candy bar daily for several weeks, and each man’s body weight was recorded. It is found that the mean change in body weight was +1.5 kg. The variance of these 20 data of weight-change has been estimated as s2 = 6.25 kg2. (50 pts) – t distribution and chi-square distribution tables are included.

1. (a) Test the null hypothesis that the candy bar has NO significant effect on body weight.

2. (b) Test the null hypothesis that the candy bar will have positive impact on the body weight

   change.

(c) Test the null hypothesis that H0: ?2 = 3.00 kg2
(d) Test the null hypothesis that H0: σ2 ≥ 5.00 kg2