8.46 A random sample of 10 miniature Tootsie Rolls was taken from a bag. Each piece was weighed on a very accurate scale. The results in grams were 3.087 3.131 3.241 3.241 3.270 3.353 3.400 3.411 3.437 3.477 (a) Construct a 90 percent confidence interval for the true mean weight. The standard error is E = 1.96(s/sqrt(n)) = 1.96[0.131989/sqrt(10)]=1.96*0.41739 =0.081808 C.I. = (x-bar-E,x-bar+E) = (3.3048-0.0818,3.3048+0.0818) (b) What sample size would be necessary to estimate the true weight with an error of ± 0.03 grams with 90 percent confidence?
Define Skewness Skewness is a measure of the asymmetry of the probability distribution of a real-valued random variable about its mean. The Skewness value can be positive or negative, or even undefined. 18. What is Standard deviation (STDEV) The standard deviation (SD) (represented by the Greek letter sigma, σ) shows how much variation from the average exists. Deviation (statistics) is the difference between the value of an observation and the mean of the population in mathematics and statistics.
2.12 b. 1.734 c. -1.740 d. 1.740 ANSWER: d -same process but now go to one tailed α=0.05 and dof = 17 4. Read the t statistic from the table of t distributions and circle the correct answer. A one-tailed test (lower tail), a sample size of 10 at a .10 level of significance; t = a. 1.383 b.
Interpret. From the scatter plot it is evident that the slope of the ‘best fit’ line is positive, which indicates that Credit Balance varies directly with Size. As Size increases, Credit Balance increases and vice versa. MINITAB OUTPUT: Regression Analysis: Credit Balance ($) versus Size The regression equation is Credit Balance ($) = 2582 + 404 Size Predictor Coef SE Coef T P Constant 2581.9 195.3 13.22 0.000 Size 404.13 51.00 7.92 0.000 S = 620.793 R-Sq = 56.7% R-Sq (adj) = 55.8% Analysis of Variance Source DF SS MS F P Regression 1 24200717 24200717 62.80 0.000 Residual Error 48 18498431 385384 Total 49 42699149 Predicted Values for New Observations New Obs Fit SE Fit 95% CI 95% PI 1 4602.6 119.2 (4363.0, 4842.2) (3331.6, 5873.6) Values of Predictors for New Observations New Obs Size 1 5.00 2. Determine the equation of the ‘best fit’ line, which describes the relationship between CREDIT BALANCE and SIZE.
The rule of thumb is that the number of observations should be greater than 30 to assume a normal, symmetric population without outliers in the data set. Each of our team’s data sets contains data that is greater than 30 and in some cases is much larger. Given that the literacy populations being researched tend to be skewed, the larger population sizes we used in our research support our confidence interval computations reliability. Confidence interval is a measure of how reliable the data survey is and will likely include unknown population parameters. When the confidence interval is graphed one can determine if there is a wide range of unknown population parameters.
(b) One correct answer to this part is as follows: We can say that we are 95 percent confident the average balance for all overdue bills is in the range from $480 to $520. Since the standard error SE for the sample mean should equal 100/square root of 100 = 10, the margin of error would be twice this value, or $20. This means $480 to $520 is a 95 percent confidence interval for the average of all overdue balances. Another correct answer to this part is as follows: Instead of the average balance, we can find the percentage of all balances that fall in this interval. When we think of all balances, $480 is 0.2 standard deviations below the average (480 -500)/100 = - 0.20), and $520 is 0.2 standard deviations above the average (520 -500)/100 = 0.20).
AP Statistics Name _______________ 3/24/09 Wood/Myers Period _____ Test #12 (Chapter 13) Honor Pledge __________ Part I - Multiple Choice (Questions 1-10) – Circle the letter of the answer of your choice. 1. An SRS of size 100 is taken from a population having proportion 0.8 successes. An independent SRS of size 400 is taken from a population having proportion 0.5 successes. The sampling distribution for the difference in sample proportions has what standard deviation?
The formula S = C (1 + r)^t models inflation, where C = the value today r = the annual inflation rate S = the inflated value t years from now Use this formula to solve the following problem: If the inflation rate is 3%, how much will a house now worth $510,000 be worth in 5 years? 510000(1ⓜ┤+ⓜ0.03)^5 =591229.777893 591229.77789300005 Write 6 = log2 64 in its equivalent exponential form. 26=64 Write 8y = 300 in its equivalent logarithmic form. log 300 = log 8y log(3*100)=log 8y log 3+log100=log 8+log y log 3+2=log 8+log y log 8-log 3=log y-2 By log(A/B)=log A-log B, log (8/3)=log y-2 Hurricanes are some of the largest storms on earth. They are very low pressure areas with diameters of over 500 miles.
Prior to implementing this system, a manual system was used. The distribution of the number of errors per invoice for the manual system is as follows: Errors per invoice 0 1 2 3 More Than 3 Percentage of Invoices 87% 8% 3% 1% 1% After implementation of the computerized system, a random sample of 500 invoices gives the following error distribution: Errors per invoice 0 1 2 3 More Than 3 Numbers of Invoices 479 10 8 2 1 a. Show that it is appropriate to carry out a chi-square test using these data. n*p0=500*0.87=435 n*p1=500*0.08=40 n*p2=500*0.03=15 n*p3=500*0.01=5 n*p4=500*0.01=5 all of them are greater
c) Suggest a different approximation, compute the regression equation, coefficient of determination and compare it with results in a) and b). d) Explain the nature of this relationship. Quantity demanded | Average annual income | 250 | 28123 | 330 | 32350 | 360 | 33495 | 380 | 33540 | 400 | 33999 | 400 | 34120 | 410 | 39954 | 440 | 40091 | 440 | 41650 | 440 | 41840 | 445 | 41956 | 450 | 42500 | 460 | 42900 | 470 | 43254 | 480 | 44001 | 500 | 44931 | 500 | 45125 | 520 | 47012 | Given data Resolution A: a) and b) Make a graph and suggest a simple regression model for the data below. Compute the coefficient of determination and explain the result. This linear equation shows the increase of average annual income as the quantity demanded grows.