Two plots at Rothamsted Experimental Station were studied for production of wheat straw. For a random sample of years, the annual wheat straw production (in pounds) from one plot was as follows.

Use a calculator to verify that, for this plot, the sample variance is s² ≈ 0.294.

Another random sample of years for a second plot gave the following annual wheat production (in pounds).

Use a calculator to verify that the sample variance for this plot is s² ≈ 0.959.

Test the claim that there is a difference (either way) in the population variance of wheat straw production for these two plots. Use a 5% level of signifcance.

(a) What is the level of significance?

State the null and alternate hypotheses.

H_o: σ₁² = σ₂²; H₁: σ₁² > σ₂²H_o: σ₁² > σ₂²; H₁: σ₁² = σ₂²    H_o: σ₂² = σ₁²; H₁: σ₂² > σ₁²H_o: σ₁² = σ₂²; H₁: σ₁² ≠ σ₂²

(b) Find the value of the sample F statistic. (Use 2 decimal places.)


What are the degrees of freedom?

What assumptions are you making about the original distribution?

The populations follow independent chi-square distributions. We have random samples from each population.The populations follow independent normal distributions. We have random samples from each population.    The populations follow independent normal distributions.The populations follow dependent normal distributions. We have random samples from each population.

(c) Find or estimate the P-value of the sample test statistic. (Use 4 decimal places.)

p-value > 0.2000.100 < p-value < 0.200    0.050 < p-value < 0.1000.020 < p-value < 0.0500.002 < p-value < 0.020p-value < 0.002

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis?

At the α = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.    At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.

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

Fail to reject the null hypothesis, there is sufficient evidence that the variance in annual wheat production differs between the two plots.Reject the null hypothesis, there is insufficient evidence that the variance in annual wheat production differs between the two plots.    Reject the null hypothesis, there is sufficient evidence that the variance in annual wheat production differs between the two plots.Fail to reject the null hypothesis, there is insufficient evidence that the variance in annual wheat production differs between the two plots.

Question 14 Consider the following sample of 11 length-of-stay values (measured in days): 1, 1, 3, 3, 3, 4, 4, 4, 4, 5, 7 Now suppose that due to new technology you are able to reduce the length of stay at your hospital to a fraction 0.5 of the original values. Thus, your new sample is given by .5, .5, 1.5, 1.5, 1.5, 2, 2, 2, 2, 2.5, 3.5 Given that the standard deviation in the original sample was 1.7, in the new sample the standard deviation is _._. (Truncate after the first decimal.)

A furniture store has maintained monthly sales records for the past 20​ months, with the results shown below.

Assume you have determined there is NO SEASONALITY in this time series.​ Therefore, you want to fit a linear trend model​ (that is, trend​ only) to the data.

Calculate the linear trend equation.​ (Round coefficients to the nearest whole​ number.)

y= _+ _ * t

nothing​*t

What are the test statistic and​ p-value to test for a significant trend. Round both to two decimal places.

T​ =

​p-value =

Is the trend significant using a​ 10% significance​ level?

Yes

No

What is the value of​ R-squared? (Round to two​ decimals.)

Forecast the sales for the next month​ (t =​ 21). (Round to the nearest whole​ number.)

Upper F21=?

Based on the​ R-squared value, how confident are you in this​ forecast? (That​ is, how accurate do you think the forecasts will​ be?)

A.

Not confident at all because the​ R-squared value is so low

B.

Very confident because the​ R-squared value is high

C.

Somewhat confident because the​ R-squared value is moderate​ (not extremely high but not extemely​ low)

Click to select your answer(s).

A particular report included the following table classifying 712 fatal bicycle accidents according to time of day the accident occurred.

(a) Assume it is reasonable to regard the 712 bicycle accidents summarized in the table as a random sample of fatal bicycle accidents in that year. Do these data support the hypothesis that fatal bicycle accidents are not equally likely to occur in each of the 3-hour time periods used to construct the table? Test the relevant hypotheses using a significance level of .05. (Round your χ² value to two decimal places, and round your P-value to three decimal places.)

What can you conclude?

There is sufficient evidence to reject H₀. There is insufficient evidence to reject H₀.    

(b) Suppose a safety office proposes that bicycle fatalities are twice as likely to occur between noon and midnight as during midnight to noon and suggests the following hypothesis: H₀: p₁ = 1/3, p₂ = 2/3, where p₁ is the proportion of accidents occurring between midnight and noon and p₂ is the proportion occurring between noon and midnight. Do the given data provide evidence against this hypothesis, or are the data consistent with it? Justify your answer with an appropriate test. (Hint: Use the data to construct a one-way table with just two time categories. Use α = 0.05. Round your χ² value to two decimal places, and round your P-value to three decimal places.)

What can you conclude?

There is sufficient evidence to reject H₀. There is insufficient evidence to reject H₀.    

You may need to use the appropriate table in Appendix A to answer this question.

ou are given the sample mean and the population standard deviation. Use this information to construct the 90% and 95% confidence intervals for the population mean. Which interval is wider? If convenient, use technology to construct the confidence intervals.

A random sample of

3939

gas grills has a mean price of

$632.10632.10.

Assume the population standard deviation is

$55.6055.60.

The 90% confidence interval is (____,___)

Males in the Netherlands are the tallest, on average, in the world with an average height of 183 centimeters (cm) (BBC News website). Assume that the height of men in the Netherlands is normally distributed with a mean of 183 cm and standard deviation of 10.5 cm.

a.What is the probability that a Dutch male is shorter than 175 cm?

b.What is the probability that a Dutch male is taller than 195 cm?

c.What is the probability that a Dutch male is between 173 and 193 cm?

d.Out of a random sample of 1000 Dutch men, how many would we expect to be taller than 190 cm?

Suppose you are interested in bidding on a parcel of land and you know that one other bidder is interested. The seller has announced that the highest bid will be accepted. The other competitor’s bidding price for the land will vary evenly from $72,000 to $85,500.

1. Let B be the competitor’s bid for the parcel of land. What are the distribution and parameter(s) of B?

2. What is expected value and standard deviation of the competitor’s bid?

3. What is the probability that the competitor’s bid will be less than $80,000?

4. What values mark the middle 50% of the competitor’s bids?

5. You and the competitor each put in a sealed bid (i.e. you do not know the competitor’s bid and he does not know yours). Suppose that you bid $79,000. What is the probability that your bid will be accepted? (i.e. that yours will be higher than the competitor.)

6. The competitor has hinted that he will not go higher than $82,750. What is the probability that his actual bid is above $80,200?

Directions: Use the following information to complete the assignment. While APA format is not required for the body of this assignment, solid academic writing is expected, and documentation of sources should be presented using APA formatting guidelines, which can be found in the APA Style Guide, located in the Student Success Center.

A researcher randomly assigns 33 subjects to one of three groups. Group 1 receives technical dietary information interactively from an on-line website. Group 2 receives the same information from a nurse practitioner, while Group 3 receives the information from a video tape made by the same nurse practitioner.

The researcher looked at three different ratings of the presentation; difficulty, usefulness, and importance to determine if there is a difference in the modes of presentation. In particular, the researcher is interested in whether the interactive website is superior because that is the most cost-effective way of delivering the information.

1. Run the appropriate analysis of the data and interpret the results.
2. How could this study have been done differently? Why or why not would this approach be better?

According to a Field Poll conducted, 79% of adults (actual results are 400 out of 506 surveyed) feel that "education and our schools" is one of the top issues facing the state. We wish to construct a 90% confidence interval for the true proportion of adults who feel that education and the schools is one of the top issues facing the state. Find a 90% confidence interval for the population proportion. Round your answers to three decimal places.

An email was randomly sent out to 150 people of various ages. I believe that more than 15% of the people being asked support the "Brand X" motorcycle. The people were asked: Out of the brands listed below, what is your preferred brand of motorcycle. Please reply with the alpha number in the subject line.

A) Honda

B)Yamaha

C) Indian

D) Harley Davidson

E) Kawasaki

F) Ducati

Results:

*Successes (x) (i.e. in for of Brand “X” = D = Harley Davidson) = 31 in favor of

*Sample size (n) = 150

SOLVE: (State hypothesis, Z-stat, rejection region, P-Value, Classic approach, reasoning)

Suppose a Department Chair randomly selects 5 new teaching assistants from a total of 20 applicants - 11 boys and 9 girls. Let x be the number of girls who are hired. Find the mean and standard deviation of random variable x.

(a) μ = 2.75 and σ = 0.9770

(b) μ = 2.25 and σ = 0.9884

(c) μ = 2.75 and σ = 0.9884

(d) μ = 2.25 and σ = 0.9770

Consider the following hypotheses:

H₀: p ≥ 0.48

H_A: p < 0.48

Compute the p-value based on the following sample information. (You may find it useful to reference the appropriate table: z table or t table) (Round "z" value to 2 decimal places. Round intermediate calculations to at least 4 decimal places and final answers to 4 decimal places.)

1. Use the data analysis package to develop the regression equation.
2. What is the r²?  And what is the standard error?  What do they mean in this example?
3. What does the slope of the line represent in this example?  Use a sentence or two to explain this.
4. What is the 95% confidence interval for the parameter β₁ ?  At the significance level of 5%, can you reject the hypothesis that β₁ = 0?

17. You run a hypothesis test to see whether the average price of gas is higher than the reported value of $2.53. You find a p-value of .001 and reject Ho. a. Which type of error could you be committing here, Type 1 or Type 2? 18. In a jury trial, the jury makes a decision, and they could be right or wrong. Describe how a type 1 error could happen in this situation, and how a type 2 error could happen in this situation. Which error do you believe is worse to commit and why? (This is just your own opinion.) 21. Bob’s local pizza place claims it delivers pizzas in 30 minutes on average. Bob is convinced it’s more than that. He does a hypothesis test and gets a p-value of .001. a. What does Bob conclude? b. If Bob made the wrong conclusion what error did he make? c. What would be the impact of his error?