The accuracy of a census report on a city in southern California was questioned by some government officials. A random sample of 1215 people living in the city was used to check the report, and the results are shown below.

Using a 1% level of significance, test the claim that the census distribution and the sample distribution agree.

(a) What is the level of significance?


State the null and alternate hypotheses.

H₀: The distributions are the same.
H₁: The distributions are the same.H₀: The distributions are different.
H₁: The distributions are different.    H₀: The distributions are the same.
H₁: The distributions are different.H₀: The distributions are different.
H₁: The distributions are the same.

(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?

YesNo    

What sampling distribution will you use?

Student's tnormal    uniformbinomialchi-square

What are the degrees of freedom?


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

P-value > 0.1000.050 < P-value < 0.100    0.025 < P-value < 0.0500.010 < P-value < 0.0250.005 < P-value < 0.010P-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 1% level of significance, the evidence is sufficient to conclude that census distribution and the ethnic origin distribution of city residents are different.At the 1% level of significance, the evidence is insufficient to conclude that census distribution and the ethnic origin distribution of city residents are different.

Please i need a detailed explanation of this short article

Thinking of the many variables tracked by hospitals and doctors' offices, confidence intervals could be created for population parameters calculated frommany of them. What variable and parameter might be most helpful in your work to be able to create an interval that captures the true value of the parameter of patients with 95% confidence?

Repeat analyses of the sulphate in ground waters using a gravimetric analysis technique yielded the following data for successive samples: 27.4, 27.6, 25.2, 27.3, 27.3 ppm sulphate. Using 95% confidence criteria which of the following statements is true?

Select one:

a. 25.2 should be rejected

b. 27.4 should be rejected

c. 25.2 and 27.4 should be rejected

d. no data should be rejected

5. A driver encounters two traffic lights on the way to work each morning. Each light is either red, yellow, or green. The probabilities of the various combinations of colors is given in the following table:

a) What is the probability that the first light is red?

b) What is the probability that the second light is green?

c) Find the probability that both lights are of the same color.

d) Given that the first light is red, find the probability that the second light is green.

Find confidence interval and perform a hypothesis test for the mean of one population.

The economic dynamism, which is the index of productive growth in dollars for countries that are designated by the World Bank as middle-income are in table #1. Countries that are considered high-income have a mean economic dynamism of 60.29. Do the data show that the mean economic dynamism of middle-income countries is less than the mean for high-income countries? Test at the 5% level.

Table #1

a) What is the appropriate test for this case?

b) What are the assumptions to run the test?

c) What is the null hypothesis?

d) What is the alternative hypothesis?

e) Determine if this test is left-tailed, right-tailed, or two-tailed.

f) What is the significance level?

g) What is the test statistics?

h) What is the p-value?

i) Do we reject the null hypothesis? Why?

j) What is the conclusion?

k) What is 95% confidence interval for the population mean?

l) Interpret the confidence interval.

The marketing manager of a large supermarket chain would like to use shelf space to predict the sales of pet food. A random sample of 12 equal-sized stores is selected, with the following results.

A. Construct a scatter plot for these data, b₀ = 145 and b₁ = 7.4.

B. Interpret the meaning of the slope, b₁, in this problem.

C. Predict the mean weekly sales (in hundreds of dollars) of pet food for stores with 8 feet of shelf space for pet food.

D. What does the coefficient of determination indicate about the independent variable?

In a genetics experiment, investigators looked at 300 chromosomes of a particular type and counted the number of sister-chromatid exchanges n each. A Poisson model was hypothesized for the distribution of the number of exchanges. Test the fit of a Poisson distribution to the data.

Read the article "Interval Training" by Christine M. Anderson-Cook. Pick an interval type and explain the concept of the interval type through an example.

In the lecture, we covered the “pooled-testing” problem, namely when you do blood test on large number of people, it is more efficient to pool k people’s blood together to do the test: if this pooled blood sample results in negative, then you know all these k people are negative, if this pooled blood sample results in positive, then you need to re-test each one of them in this group. Therefore, for each group of k people, you either test once or k+1 times. Suppose p is the rate of certain disease, in case p= 0.1, in the class, we did the calculation 0f E(X), where x is the random number of times you need to do the test. For this problem, if P= 0.05 and N=150000, do the calculation of E(X)  for k =3, 4, 5, 6, 7, 8, 10, 15, 25, 35, and then determine the best k.

I understand how to work the problem except for figuring out the z-score. Could you please explain how to find the z-score for the following problem?

The demand during the lead time is normally distributed with a mean of 40 and a standard deviation of 4. if the company wishes to maintain a 90 percent service level, how much safety stock should be held?

Mean = 40, s= 4 x= safety stock

2. You randomly select 16 cars of the same model that were sold at a car dealership and determine the number of days each car sat on the dealership’s lot before it was sold. The sample mean is 9.15 days, with a sample standard deviation of 1.6 days. Construct a 95% confidence interval for the population mean number of days the car model sits on the dealership’s lot. (10 p)

(Round off final answers to two decimal places, if appropriate. Do not round off numbers taken directly from tables).

3. A researcher collected data from a random sample of 25 high school freshmen and found the mean of the sample to be 85.40 on the Test of Critical Thinking (TCT). She also calculated the standard deviation from the sample and discovered the value was 12.30. The average score on the Test of Critical Thinking for all high school seniors in a large school district is 90.00. The researcher wants to know if the mean TCT of the 25 high school freshmen in the random sample is different from the population’s (i.e., highschool seniors) TCT mean.

(Round off final answers to two decimal places, if appropriate. Do not round off numbers taken directly from tables).

e. What decision should be made about the null hypothesis? In other words, should you reject or retain the null hypothesis? (10p)

g. Provide a brief conclusion regarding your findings. Use your power point lecture slides for writing out the interpretation of your results. (10p)

Question # 1

Rothenberg et al. (2004) investigated the effectiveness of using the Hologic Sahara Sonometer, a portable device that measures bone mineral density (BMD) in the ankle, in predicting a fracture. They used a Hologic estimated bone mineral density value of

.57 as a cutoff. The results yielded the following data:

a. Compute the Sensitivity of the test. (6 points)

b. Compute the Specificity of the test. (6 points)

c. Compute the Positive Predictive Value (6 points)

Question # 2

According to the most recent Davenport student profile, 28% of students are male. Given a sample of 15 students:

a. Find the probability that none are male. (6 points)

b. Find the probability that 10 are male. (6 points)

c. Find the probability that at least six are male. (6 points)

2. Data was collected where a weightlifter was asked to do as many repetitions as possible using different amounts of weight. Below is a table that shows how much weight was on the bar, and how many repetitions the weightlifter could do: Weight 200 300 400 500 Reps 42 27 12 3

a. Calculate the correlation for this data. What does this value tell you about the relationship between these two variables?

b. Determine the least squares regression line for this data. Interpret the values for the y-intercept and the slope within this scenario.

c. Calculate r2 for this data and describe what it represents.

d. Using the regression line from part (b), calculate the predicted number of repetitions for this weight lifter if the weight is 400 pounds, and then calculate and interpret the residual for that weight using the data.