M12 Q9

What is the optimal time for a scuba diver to be on the bottom of the ocean? That depends on the depth of the dive. The U.S. Navy has done a lot of research on this topic. The Navy defines the "optimal time" to be the time at each depth for the best balance between length of work period and decompression time after surfacing. Let x = depth of dive in meters, and let y = optimal time in hours. A random sample of divers gave the following data.

(a) Find Σx, Σy, Σx², Σy², Σxy, and r. (Round r to three decimal places.)

(b) Use a 1% level of significance to test the claim that ρ < 0. (Round your answers to two decimal places.)

Conclusion

Fail to reject the null hypothesis. There is insufficient evidence that ρ < 0.

Reject the null hypothesis. There is sufficient evidence that ρ < 0.     

Fail to reject the null hypothesis. There is sufficient evidence that ρ < 0.

Reject the null hypothesis. There is insufficient evidence that ρ < 0.

(c) Find S_e, a, and b. (Round your answers to five decimal places.)

(d) Find the predicted optimal time in hours for a dive depth of x = 22 meters. (Round your answer to two decimal places.)
hr

(e) Find an 80% confidence interval for y when x = 22 meters. (Round your answers to two decimal places.)

(f) Use a 1% level of significance to test the claim that β < 0. (Round your answers to two decimal places.)

Conclusion

Fail to reject the null hypothesis. There is insufficient evidence that β < 0.

Reject the null hypothesis. There is sufficient evidence that β < 0.     

Reject the null hypothesis. There is insufficient evidence that β < 0.

Fail to reject the null hypothesis. There is sufficient evidence that β < 0.

(g) Find a 90% confidence interval for β and interpret its meaning. (Round your answers to three decimal places.)

Interpretation

For a 1 meter increase in depth, the optimal time increases by an amount that falls within the confidence interval.

For a 1 meter increase in depth, the optimal time decreases by an amount that falls outside the confidence interval.     

For a 1 meter increase in depth, the optimal time decreases by an amount that falls within the confidence interval.

For a 1 meter increase in depth, the optimal time increases by an amount that falls outside the confidence interval.

1)With​ two-way ANOVA, the total sum of squares is portioned in the sum of squares for​ _______.

2) A​ _______ represents the number of data values assigned to each cell in a​ two-way ANOVA table. a)cell b) Block c)replication D)level

3.) True or false: In a​ two-way ANOVA​ procedure, the results of the hypothesis test for Factor A and Factor B are only reliable when the hypothesis test for the interaction of Factors A and B is statistically insignificant.

4.)Randomized block ANOVA partitions the total sum of squares into the sum of squares​ _______. A)between, within B)Between, within, block C)Between, Block, error D)Between,within, error

You wish to test the following claim (HaHa) at a significance level of α=0.005α=0.005. For the context of this problem, μd=μ2−μ1μd=μ2-μ1 where the first data set represents a pre-test and the second data set represents a post-test.

      Ho:μd=0Ho:μd=0
      Ha:μd>0Ha:μd>0

You believe the population of difference scores is normally distributed, but you do not know the standard deviation. You obtain pre-test and post-test samples for n=264n=264 subjects. The average difference (post - pre) is ¯d=3.6d¯=3.6 with a standard deviation of the differences of sd=20.4sd=20.4.

What is the test statistic for this sample? (Report answer accurate to three decimal places.)
test statistic =

What is the p-value for this sample? (Report answer accurate to four decimal places.)
p-value =

The p-value is...

• less than (or equal to) αα
• greater than αα

This test statistic leads to a decision to...

• reject the null
• accept the null
• fail to reject the null

As such, the final conclusion is that...

• There is sufficient evidence to warrant rejection of the claim that the mean difference of post-test from pre-test is greater than 0.
• There is not sufficient evidence to warrant rejection of the claim that the mean difference of post-test from pre-test is greater than 0.
• The sample data support the claim that the mean difference of post-test from pre-test is greater than 0.
• There is not sufficient sample evidence to support the claim that the mean difference of post-test from pre-test is greater than 0.

The values of Alabama building contracts (in $ millions) for a 12‐month period follow: (19 marks total)
240 350 230 260 280 320 220 310 240 310 240 230
a. Construct a time series plot. What type of pattern exists in the data?
b. Compare the three‐month moving average approach with the exponential smoothing forecast using α=0.4. Which approach provides more accurate forecasts based on MSE? c. What is the forecast for the next month?
d. Explain how you would find the optimum level of α for this data.
Please answer this question at α=0.4. I have submission deadline of 3 hrs. Also if possible please post the solution typed.

The Economic Policy Institute reports that the average entry-level wage for male college graduates is $22.07 per hour and for female college graduates is $19.85 per hour. The standard deviation for male graduates is $3.77 and for female graduates is $3.11. Assume wages are normally distributed. Question 1: If 25 females graduates are chosen, find the probability the sample average entry-level wage is at least $20.60.

Data on the gasoline tax per gallon (in cents) as of a certain date for the 50 U.S. states and the District of Columbia are shown below.

How do you know if they are outliers? (Enter your answers to two decimal places.)

To be an outlier, an observation would have to be greater than? or less than?

Comment on the interesting features of the plot. (Round numerical answers to the nearest cent.)

The boxplot shows that a typical gasoline tax is around ___ cents per gallon

In order to control costs, a company wishes to study the amount of money its sales force spends entertaining clients. The following is a random sample of six entertainment expenses (dinner costs for four people) from expense reports submitted by members of the sales force

(a) Calculate x¯x¯ , s², and s for the expense data. (Round "Mean" and "Variances" to 2 decimal places and "Standard Deviation" to 3 decimal places.)

(b) Assuming that the distribution of entertainment expenses is approximately normally distributed, calculate estimates of tolerance intervals containing 68.26 percent, 95.44 percent, and 99.73 percent of all entertainment expenses by the sales force. (Round intermediate calculations and final answers to 2 decimals.)

(c) If a member of the sales force submits an entertainment expense (dinner cost for four) of $390, should this expense be considered unusually high (and possibly worthy of investigation by the company)? Explain your answer.

(d) Compute and interpret the z-score for each of the six entertainment expenses. (Round z-score calculations to 2 decimal places. Negative amounts should be indicated by a minus sign.)

Provide an example of how standard deviation is used to measure sports statistics (other than the examples in the book). Feel free to use an example outside of sports. (econ of sports)

According to the National Center for Education Statistics, 69% of Texas students are eligible to receive free or reduced-price lunches. Suppose you randomly choose 285 Texas students. Find the probability that no more than 73% of them are eligible to receive free or reduced-price lunches.

Based on historical data, your manager believes that 34% of the company's orders come from first-time customers. A random sample of 122 orders will be used to estimate the proportion of first-time-customers. What is the probability that the sample proportion is greater than than 0.21?

Note: You should carefully round any z-values you calculate to 4 decimal places to match wamap's approach and calculations.

Answer = (Enter your answer as a number accurate to 4 decimal places.)

Based on historical data, your manager believes that 32% of the company's orders come from first-time customers. A random sample of 138 orders will be used to estimate the proportion of first-time-customers. What is the probability that the sample proportion is between 0.21 and 0.35?

Note: You should carefully round any z-values you calculate to 4 decimal places to match wamap's approach and calculations.

Answer = (Enter your answer as a number accurate to 4 decimal places.)

An investment advisor claimed that BIT return is 2%. Do you agree? Justify your reasoning using a two-tailed hypothesis test approach at the significance level of 5% in Excel.

Exhibit 1:  

We have the following information about number of violent crimes (Y) and the number of police personnel (X) for a certain year for a sample of three metropolitan areas. We also know the following statistics: SST = 1250, SSE = 937.5

Question 6

1. To answer this question, refer to Exhibit 1 in question 1.

   What does value of r² tell you?

   A.		25 percent of variation in crime is explained by the number of police personnel.
   B.		50 percent of variation in crime is explained by the number of police personnel.
   C.		75 percent of variation in crime is explained by the number of police personnel.
   D.		None of the above

Question 7

1. To answer this question, refer to Exhibit 1 in question 1.

   The coefficient of correlation is (to 2 decimal places)

   A.		0.87
   B.		-0.87
   C.		0.5
   D.		-0.5

Question 8

1. To answer this question, refer to Exhibit 1 in question 1.

   What is the estimate of the standard error of the overall regression (to 2 decimal places)?

   		10.91
   		30.62
   		45.88
   		55.67

Question 9

1. To answer this question, refer to Exhibit 1 in question 1.

   What is the estimate of the standard error of slope estimate (to 3 decimal places)?

   		0.001
   		0.015
   		0.022
   		0.053

Question 10

1. To answer this question, refer to Exhibit 1 in question 1.

   Is police personnel a significant variable affecting crime in the above data?

   		No because we cannot reject the null the slope is 0.
   		Yes because we can reject the null the slope is 0.
   		Need more information to answer the question

The ability to scale up renewable energy and in particular wind power and speed is dependent on the ability to forecast its short term availability soman et al (2010( describe different methods for wind power forecasting (the quote is slightly edited for brevity)

Persistence method: this method is also known as ‘naïve predictor. Its is assumed that the wind speed at time t + tetat will be the same as it was at time t. unbelievably it is more accurate than most of the physical and statistical methods for very short to short term forecasts.

Physical approach: physical systems. Use parameterizations based on a detailed physical description of the atmosphere

Statistical approach: the statistical approach is based on training with measurement data and uses difference between the predicted and the actual wind speeds in immediate past to tune model parameters. It is easy to model, inexpensive, predefined mathematical model and rather it is based on patterns

Hybrid approach: In general, the combination of different approaches such as mixing physical and statistical approaches or combining short term and medium term models etc is referred to as a hybrid approach.

1. For each of the four types of methods, describe whether it is model- based, data -driven, or a combination.
2. For each of the four types of methods, describe whether it is based on extrapolation, causal modeling, correlation modeling or a combination.
3. Describe the advantages and disadvantages of the hybrid approach

You take a quiz with 6 multiple choice questions. After you​ studied, you estimated that you would have about an​ 80% chance of getting any individual question right. What are your chances of getting them all​ right? The random numbers below represent a simulation with 20 trials. Let​ 0-7 represent a correct answer and let​ 8-9 represent an incorrect answer.

1, 6   5   6   2   0   5
2, 4   7   3   1   6   6
3, 5   2   9   6   3   2
4, 8   0   1   6   0   8
5, 3   4   3   3   4   4
6, 2   9   1   7   3   0
7, 6   5   9   6   8   3
8, 8   6   4   4   2   7
9, 6   1   1   8   2   6
10, 5   3   0   3   8   6
11, 0   2   8   1   3   2
12, 6   8   6   0   0   4
13, 9   9   4   6   1   8
14, 1   7   3   2   5   1
15, 7   6   6   1   4   5
16, 3   5   3   1   4   5
17, 0   2   7   7   3   1
18, 3   6   1   6   1   0
19, 8   4   6   7   1   3
20, 5   3   5   2   0   9

A local university found it could classify its students into one of three general categories: morning students (42%), afternoon students (33%), and evening students. 37% of the morning students, 23% of the afternoon students, and 16% of the evening students live on campus. What is the probability a non-evening student does not live on campus?