I tried to graph the following data in excel to obtain the equation of the line which happens to be polynomial 4th order

I am given a R.I of 1.3616 and expected to obtain Vol% by solving the polynomial. i did that with excel and got 9.2 and the correct answer is around (you can guess by liner interpolation) is 63.

here's the polynomial : R.I= 1.3323+6.9476e(-4)X-4.711e(-6)X^2+3.7995e(-5)X^3-3.2634e(-10)X^4

can anyone do hand calculation and excel to confirm this

Break a stick of unit length at a uniformly chosen random point. Then take the shorted of the two pieces and break it again in two pieces at a uniformly chosen random point. Let X denote the shortest of the final three pieces. Find the density of X.

Determine if a statistically significant linear relationship exists between the independent and dependent variables at the 0.01 level of significance. If the relationship is statistically significant, identify the multiple regression equation that best fits the data, rounding the answers to three decimal places. Otherwise, indicate that there is not enough evidence to show that the relationship is statistically significant.

A doctor wants to estimate the mean HDL cholesterol of all​ 20- to​ 29-year-old females. How many subjects are needed to estimate the mean HDL cholesterol within 3 points with 99% confidence assuming s=12.5 based on earlier​ studies? Suppose the doctor would be content with 90% confidence. How does the decrease in confidence affect the sample size​ required?

1. Now assume that Data Set A depicts the scores of five subjects who received both Treatment 1 and Treatment 2. Calculate a t-test for dependent means to determine whether the means for the two treatments were significantly different. The correlation between the two treatments is +1.00. In your complete answer, remember to include your t-statistic, critical value, and your decision about whether to reject the null hypothesis. For this question, you should assume that the same participants received each of the two treatments. (15 points)

Take a moment to reflect on what you have learned in this module about hypothesis testing in general and A/B testing in particular.

- In what other scenarios or industries do you think this type of analysis would be helpful?

- What precautions should you take when designing such tests?

- How can you ensure that your results are representative of your target population?

The design of an automotive gear requires the diameter to be 4 inches. To evaluate the production quality, you sample 30 gears and find the average to be 4.08 with a standard deviation of 0.71. Construct a hypothesis test at a 0.05 level of significance to determine if the gear diameter is larger than 4 inches.

Select one:

a. The critical value is 1.70, the test statistic is 0.62, conclude the gear diameter is less than or equal to 4 inches

b. The critical value is 1.70, the test statistic is 0.62, conclude the gear diameter is greater than 4 inches

c. The critical value is 2.05, the test statistic is 0.62, conclude the gear diameter is greater than 4 inches

d. The critical value is 2.05, the test statistic is 0.62, conclude the gear diameter is less than or equal to 4 inches

e. The critical value is 2.05, the test statistic is 0.62, conclude the gear diameter is not equal to 4 inches

General HyThere, Inc., is a manufacturer of hydraulic machine tools. It has had a history leakage trouble resulting from a certain critical fitting. Twenty five samples of machined parts were selected, one per shift, and the diameters of the fitting was measured.

Required:

a. Construct x-bar- and R-charts for the data. What do you observe?

b. If the regular machine operator was absent when samples 4, 8, 14, 22 were taken, how will the results in part (a) be affected?  

c. A second table in the worksheet represents measurements taken during the next 10 shifts. Does the process continue to remain stable? What information does this table provide to the quality control manager?  

Can you show how you entered the data into excel to get the graphs please.

Upload Cars04-1 Cars04-1 data and use engine size to predict the car’s city gas mileage(City MPG). Answer the questions.

I) For each additional 2.0 liter in engine size how much the MPG will change? (11.11 points)

• a. It will decrease by 0.21 mpg.
• b. It will decrease by 8.21 mpg.
• c. It will be 25.49 mpg.
• d. For car with zero horse power we expect 33.7 mpg.
• e. Not applicable.

II) After performing the regression analysis you are asked to pick one number that would best answer the question: Are these two variables, engine size and city gas mileage, related or not? What is this number and why?  (11.11 points)

• a. The number is the P-value, which in this case is very low indicating a strong probability that the two variables are related.
• b. The number is the slope and it clearly indicates the relation: For each additional liter in engine size the mpg decreases.
• c. This number is R-square and since it is not close to 1 we cannot claim that these two variables are related.
• d. None of these.

III) Given a car that has the engine size of 3.0 liters use regression analysis and all available information in there, in order to predict this car’s city gas mileage. What is your interval prediction? (11.11 points)

• a. ±4.15
• b. 33.7
• c. 21.38
• d. [17.09, 25.68]
• e. Not applicable

  EngineSize	CityMPG
  1.6	28
  1.6	28
  2.2	26
  2.2	26
  2.2	26
  2	29
  2	29
  2	26
  2	27
  2	26
  2	26
  1.7	32
  1.7	36
  1.7	32
  1.6	29
  1.6	29
  1.6	29
  2	26
  2	26
  2	26
  2.4	23
  1.6	26
  1.6	25
  1.8	24
  1.8	24
  1.8	24
  1.6	28
  1.8	28
  1.8	28
  2.2	24
  2.2	26
  2.2	26
  2.2	26
  2.2	26
  2.2	26
  1.5	32
  2.3	25
  2.3	25
  2	24
  2	22
  1.8	32
  1.8	32
  1.8	32
  1.5	35
  1.5	33
  1.5	35
  3.1	20
  3.4	21
  2.2	24
  3.5	22
  3.4	21
  2.4	22
  2.4	22
  2.4	22
  2.7	21
  2.7	21
  2.4	21
  2.4	21
  2	21
  3	20
  3	19
  2.4	26
  2.4	26
  1.7	32
  2	26
  1.4	46
  2	60
  2.7	19
  2.7	19
  2.7	20
  2.3	24
  3	20
  1.6	25
  2.5	21
  2.5	23
  2.2	24
  3.4	20
  3.8	20
  2.2	24
  3	20
  2.5	22
  2.5	21
  2.5	20
  2.4	24
  3	21
  2.4	24
  3.3	20
  1.5	59
  2	24
  1.8	24
  1.9	38
  1.8	24
  2	24
  2.4	22
  1.8	22
  2.5	20
  3.8	20
  3.8	20
  3.8	18
  3.8	20
  3.8	18
  3.5	23
  3.8	18
  3.5	18
  2.7	21
  3.5	19
  2.4	21
  2.4	22
  3.5	18
  4.6	17
  4.6	17
  3	21
  3	21
  3.5	17
  3.5	17
  3.5	18
  3.5	18
  2.5	18
  1.8	22
  3.2	19
  4.6	17
  4.6	17
  3	19
  3.5	18
  3.8	18
  3.5	21
  3.5	20
  3.5	20
  3.4	20
  3.8	20
  2.5	21
  2.5	20
  3	19
  3	21
  3	21
  3.3	20
  2.8	21
  2	24
  1.8	22
  1.9	22
  3.2	20
  1.8	23
  3	20
  3	17
  3	18
  3	20
  3	18
  2.5	20
  2.5	19
  2.5	19
  3	20
  3	20
  3	20
  2.5	19
  3.8	20
  3.8	20
  3.6	18
  3.5	18
  2.7	21
  4.6	17
  3.5	18
  3.5	19
  3	18
  3.3	20
  3	18
  3	18
  3	20
  3	20
  2.6	20
  2.6	19
  3.2	19
  3.2	20
  4.6	17
  4.6	17
  2	20
  2	20
  2.3	21
  2.3	21
  3	19
  3	21
  2.8	19
  4	18
  2.5	20
  2.3	20
  2.5	18
  2.9	20
  2.5	20
  3.5	18
  3.5	18
  3	20
  3	18
  2.7	18
  4.2	17
  4.2	17
  4.2	14
  3	19
  3	20
  4.4	18
  4.4	18
  4.4	18
  3.8	18
  4.6	18
  4.6	18
  4.6	18
  4.5	17
  4.5	17
  3	18
  4.2	18
  4.2	17
  4.2	18
  4.2	18
  4.2	17
  3	18
  4.3	18
  4.3	18
  3.9	17
  3.9	17
  4.6	17
  4.6	17
  4.6	17
  3.2	16
  5	16
  5.5	13
  3.2	20
  5	17
  3.2	19
  5	16
  4.3	18
  5	16
  2	21
  2	21
  2.4	21
  2.3	20
  2.9	19

1. The U.S. Census Bureau computes quarterly vacancy and homeownership rates by state and metropolitan statistical areas. The following data are the rental vacancy rates in percentage (%) grouped by region for the last quarter of 2018 using a sample of 4 statistical metropolitan areas.

                                     Vacancy rates (%)

1. You are hired as statistician to test whether there are any differences among the regions regarding vacancy rates and you should allow for 10% error.
2. Do you think that the mean vacancy rate is the same for these regions? Why

Blood fat content may be influenced by many factors including age and weight. A nutritionist collected data on blood fat content, age and weight from sample of people. The data are saved in the file Assn1Q4.sav. The aim was to investigate how blood fat content is related to age and weight of individuals. 

1. ^{[1 pt.]}Check if the linear regression is appropriate to model the blood fat content depending on age and weight?

^{[1 pt.]} Give the estimated egression equation of Blood fat on the age and the weight.

3. ^{[1 pts.]} Interpret the coefficient of age.

4. ^{[1 pts.]} Test the validity of the model given in (b).

5. ^{[1 pt.]} Test (at 2% level) whether the effect of age is significant on the blood fat.

6. ^{[1 pt.]} Find the coefficient of determination? Explain this value with respect to predictive power of the estimated regression model.

Please solve and mentioned the steps in SPSS. The question is fine, a scatter plot should do to check the interact.

In order to test whether camshafts are being manufactured to specification a sample of n = 50 camshafts are selected at random. The average value of the sample is calculated to be 4.38 mm and the depths of the camshafts in the sample vary by a standard deviation of s = 0.42 mm.
Test the hypotheses selected previously, by filling in the blanks in the following:

• An estimate of the population mean is .
• The standard error is .
• The distribution is  (examples: normal / t12 / chisquare4 / F5,6).

The test statistic has value TS=  .
Testing at significance level α = 0.01, the rejection region is:
less than  and greater than  (2 dec places).
Since the test statistic  (is in/is not in) the rejection region, there (is evidence/is no evidence) to reject the null hypothesis, H ₀.
There  (is sufficient/is insufficient) evidence to suggest that the average hardness depth, μ, is different to 4.5 mm.

Were any assumptions required in order for this inference to be valid?
a: No - the Central Limit Theorem applies, which states the sampling distribution is normal for any population distribution.
b: Yes - the population distribution must be normally distributed.
Insert your choice (a or b): .

If two samples A and B had the same mean and standard deviation, but sample A had a larger sample size, which sample would have the wider 95% confidence interval? Homework Help: Sample B as it has the smaller sample Sample B as its sample is more dispersed Sample A as it has the larger sample Sample A as it comes first

A personnel manager has found that historically the scores on aptitude test given to applicants for entry level positions follow a normal distribution. A random sample of nineteen test scores from the current group of applicants had a sample mean score of 187.9 points and sample standard deviation as 32.4 points.

a. Find the margin of error.

b. Construct a confidence interval estimate for population mean with 80 percent level of confidence.

c. Construct a confidence interval estimate for population mean with 85 percent level of confidence.

Let x represent the number of mountain climbers killed each year. The long-term variance of x is approximately σ² = 136.2. Suppose that for the past 9 years, the variance has been s² = 113.4. Use a 1% level of significance to test the claim that the recent variance for number of mountain-climber deaths is less than 136.2. Find a 90% confidence interval for the population variance.

(a) What is the level of significance?


State the null and alternate hypotheses.

H_o: σ² = 136.2; H₁: σ² ≠ 136.2

H_o: σ² = 136.2; H₁: σ² < 136.2    

H_o: σ² = 136.2; H₁: σ² > 136.2

H_o: σ² < 136.2; H₁: σ² = 136.2

(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 normal population distribution.    

We assume a binomial population distribution.

We assume a uniform population distribution.

(c) Find or estimate the P-value of the sample test statistic.

P-value > 0.100

0.050 < P-value < 0.100    

0.025 < P-value < 0.050

0.010 < P-value < 0.025

0.005 < P-value < 0.010

P-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 variance for number of mountain climber deaths is less than 136.2

At the 1% level of significance, there is sufficient evidence to conclude that the variance for number of mountain climber deaths is less than 136.2    

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

Interpret the results in the context of the application.

We are 90% confident that σ² lies outside this interval.

We are 90% confident that σ² lies above this interval.    

We are 90% confident that σ² lies below this interval.

We are 90% confident that σ² lies within this interval.