“Suppose you are an educational researcher who wants to increase the science test scores of high school students. Based on tremendous amounts of previous research, you know that the national average test score for all senior high school students in the United States is 50 with a standard deviation of 20.

“Write H0 next to the verbal description of the null hypothesis and H1 next to the research hypothesis.
_____The population of students who receive tutoring will have a mean science test score that is equal to 50.
_____The population of students who receive tutoring will have a mean science test score that is greater than 50.
_____The population of students who receive tutoring will not have a mean science test score that is greater than 50.
_____The population of students who receive tutoring will have a mean science test score that is less than 50.”

A factor in determining the usefulness of an examination as a measure of demonstrated ability is the amount of spread that occurs in the grades. If the spread or variation of examination scores is very small, it usually means that the examination was either too hard or too easy. However, if the variance of scores is moderately large, then there is a definite difference in scores between "better," "average," and "poorer" students. A group of attorneys in a Midwest state has been given the task of making up this year's bar examination for the state. The examination has 500 total possible points, and from the history of past examinations, it is known that a standard deviation of around 60 points is desirable. Of course, too large or too small a standard deviation is not good. The attorneys want to test their examination to see how good it is. A preliminary version of the examination (with slight modifications to protect the integrity of the real examination) is given to a random sample of 20 newly graduated law students. Their scores give a sample standard deviation of 64 points. Using a 0.01 level of significance, test the claim that the population standard deviation for the new examination is 60 against the claim that the population standard deviation is different from 60.

(a) What is the level of significance?


State the null and alternate hypotheses.

H_o: σ = 60; H₁: σ > 60H_o: σ = 60; H₁: σ < 60    H_o: σ > 60; H₁: σ = 60H_o: σ = 60; H₁: σ ≠ 60

(b) Find the value of the chi-square statistic for the sample. (Round your answer to two decimal places.)


What are the degrees of freedom?


What assumptions are you making about the original distribution?

We assume a exponential population distribution.We assume a binomial population distribution.    We assume a normal population distribution.We assume a uniform population distribution.

(c) Find or 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?

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, there is insufficient evidence to conclude that the standard deviation of test scores on the preliminary exam is different from 60.At the 1% level of significance, there is sufficient evidence to conclude that the standard deviation of test scores on the preliminary exam is different from 60.    

(f) Find a 99% confidence interval for the population variance. (Round your answers to two decimal places.)

(g) Find a 99% confidence interval for the population standard deviation. (Round your answers to two decimal places.)

An article describes an experiment to determine the effectiveness of mushroom compost in removing petroleum contaminants from soil. Out of 155 seeds planted in soil containing 3% mushroom compost by weight, 74 germinated. Out of 155 seeds planted in soil containing 5% mushroom compost by weight, 86 germinated. Can you conclude that the proportion of seeds that germinate differs with the percent of mushroom compost in the soil? Find the P-value and state a conclusion.

The National Institute on Alcohol Abuse and Alcoholism defines binge drinking as a pattern of drinking that brings blood alcohol concentration (BAC) levels to 0.08g/dL. It is cited as the most common and deadly pattern of alcohol abuse in the country, which can cause many health problems such as alcohol poisoning, sudden infant death syndrome, and chronic diseases, to name a few. In the binge drinking fact sheet published by the Center for Disease Control and Prevention, the amount of binge drinks consumed per year by binge drinkers are greater among those with lower incomes (below $75000) and educational level. In order to verify if this claim is true, a random sample of binge drinkers from the two income groups were obtained, and the data are summarized in the table below:

Conduct a test of hypothesis at 5% level of significance to verify the claim.

What is your conclusion in the context of the problem?

What is the income distribution of super shoppers? A supermarket super shopper is defined as a shopper for whom at least 70% of the items purchased were on sale or purchased with a coupon. In the following table, income units are in thousands of dollars, and each interval goes up to but does not include the given high value. The midpoints are given to the nearest thousand dollars. Income range 5-15 15-25 25-35 35-45 45-55 55 or more Midpoint x 10 20 30 40 50 60 Percent of super shoppers 20% 14% 22% 17% 20% 7%

A red and a green die are rolled. Chart or graph the sample space, and find the odds that the numbers on the dice differ by 1 or more

In a random sample of 85 automobile engine crankshaft bearings, 10 have a surface finish that is rougher than the specifications allow.

1. Construct a 95% two-sided confidence interval for the true proportion of bearings in the population that exceeds the roughness specification.

2. How large a sample is required if we want to be 95% confident that the error in using the sample proportion to estimating the ture value p is less than 5%?

3. How large must the sample be if we wish to be at least 95% confident that the error in estimating the true proportion is less than 5% regardless of the true value of P ?

Question 2:

What is the difference between point estimation and interval estimation?

What is margin of error?

Why do we need margin of error in statistics?

Hello, I have a question, however, it is regarding a data set and doing calculations on spss. If I copy and paste my data set, it is too large of a message. How else can I get the data set to you so I can actually ask my question? Can I download an attachment to whoever will answer the question?

Dual-energy X-ray absorptiometry (DXA) is a technique for measuring bone health. One of the most common measures is total body bone mineral content (TBBMC). A highly skilled operator is required to take the measurements. Recently, a new DXA machine was purchased by a research lab and two operators were trained to take the measurements. TBBMC for eight subjects was measured by both operators. The units are grams (g). A comparison of the means for the two operators provides a check on the training they received and allows us to determine if one of the operators is producing measurements that are consistently higher than the other. Here are the data:

(a) Take the difference between the TBBMC recorded for Operator 1 and the TBBMC for Operator 2. (Use Operator 1 minus Operator 2. Round your answers to four decimal places.)

Describe the distribution of these differences using words.

The distribution is left skewed.

or

The distribution is Normal.  

or

The sample is too small to make judgments about skewness or symmetry.

or

The distribution is uniform.

or

The distribution is right skewed.

(b) Use a significance test to examine the null hypothesis that the two operators have the same mean. Give the test statistic. (Round your answer to three decimal places.)
t =

Give the degrees of freedom.


Give the P-value. (Round your answer to four decimal places.)


Give your conclusion.

We can reject H₀ based on this sample.

or

We cannot reject H₀ based on this sample.    

(c) The sample here is rather small, so we may not have much power to detect differences of interest. Use a 95% confidence interval to provide a range of differences that are compatible with these data. (Round your answers to four decimal places.)

(d) The eight subjects used for this comparison were not a random sample. In fact, they were friends of the researchers whose ages and weights were similar to the types of people who would be measured with this DXA. Comment on the appropriateness of this procedure for selecting a sample, and discuss any consequences regarding the interpretation of the significance testing and confidence interval results.

The subjects from this sample, test results, and confidence interval are representative of future subjects

or

.The subjects from this sample may be representative of future subjects, but the test results and confidence interval are suspect because this is not a random sample.

A population has a mean of 300 and a standard deviation of 90. Suppose a sample of size 100 is selected and is used to estimate . Use z-table. What is the probability that the sample mean will be within +/- 3 of the population mean (to 4 decimals)? (Round z value in intermediate calculations to 2 decimal places.) What is the probability that the sample mean will be within +/- 19 of the population mean (to 4 decimals)? (Round z value in intermediate calculations to 2 decimal places.)

Q. 1.  Suppose a population was normally distributed with a mean of 10 and a standard deviation of 2. What proportion of the scores is below 12.5?

Q.2. Let’s say that the average IQ of a group of people is 105 with a standard deviation of 15. What is the standardized (or z- score) of someone:

(a)  with an IQ of 93?

(b)  with an IQ of 135?

No handwriting please, or make it clear

thanks

A survey showed that 79​% of adults need correction​ (eyeglasses, contacts,​ surgery, etc.) for their eyesight. If 20 adults are randomly​ selected, find the probability that no more than 1 of them need correction for their eyesight. Is 1 a significantly low number of adults requiring eyesight​ correction? The probability that no more than 1 of the 20 adults require eyesight correction is nothing.

A public accounting firm requires the following activities

for an audit:

1. Draw a network for this project? (Marks 0.5)
2. Make a forward pass and a backward pass to determine ES, LS, EF, and LF? (Marks 0.5)
3. What are the critical path? (Marks 0.5)

Sequence the jobs shown below by using a Gantt chart. Assume that the move time between machines is one hour. Sequence the jobs in priority order 1, 2, 3, 4.

1. Using finite capacity scheduling, draw a Gantt chart for the schedule (Marks 0.5)
2. What is the makespan? (Marks 0.5)
3. How much machine idle time is there? (Marks 0.5)
4. How much idle time (waiting time) is there for each job? (Marks 0.5)
5. When is each job delivered? (Marks 0.5)
6. Which department is the bottleneck? (Marks 0.5)
7. Calculate the machine utilization? (Marks 0.5)