Given that Z is a standard normal random variable, the area to the left of a value z is expressed as: a. OP(0 ≤ Z ≤ z) b. OP(Z > Z) c. OP(Z < Zz) d. OP(Z > -z) e. OP(Z < Z ≤ 0)
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- Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s pole vault height has fallen below the value predicted by the regression line in Example 2. This might have occurred because when the pole vault was a new event there was much room for improvement in vaulters’ performances, whereas now even the best training can produce only incremental advances. Let’s see whether concentrating on more recent results gives a better predictor of future records. (a) Use the data in Table 2 (page 176) to complete the table of winning pole vault heights shown in the margin. (Note that we are using x=0 to correspond to the year 1972, where this restricted data set begins.) (b) Find the regression line for the data in part ‚(a). (c) Plot the data and the regression line on the same axes. Does the regression line seem to provide a good model for the data? (d) What does the regression line predict as the winning pole vault height for the 2012 Olympics? Compare this predicted value to the actual 2012 winning height of 5.97 m, as described on page 177. Has this new regression line provided a better prediction than the line in Example 2?Q4. Using the listed duration and interval after times, find the best predicted “interval after”time for an eruption with a duration of 253 seconds. How does it compare to an actual eruptionwith a duration of 253 seconds and an interval after time of 83 minutes?Duration 242 255 227 251 262 207 140IntervalAfter91 81 91 92 102 94 91 a) Find the value of the linear correlation coefficient ?b) Find the critical values of r from table A-6 using ∝= 0.05c) Determine whether there is sufficient evidence to support a claim of a linear correlationBetween the two variables.Q4. Using the listed duration and interval after times, find the best predicted “interval after”time for an eruption with a duration of 253 seconds. How does it compare to an actual eruptionwith a duration of 253 seconds and an interval after time of 83 minutes?Duration 242 255 227 251 262 207 140IntervalAfter91 81 91 92 102 94 91 a) Find the value of the linear correlation coefficient ?b) Find the critical values of r from table A-6 using ∝= 0.05c) Determine whether there is sufficient evidence to support a claim of a linear correlationBetween the two variables.d) Find the regression equation,e) Letting the first variable be the predictor (x) variable, find the indicated predicted value.
- An emergency service wishes to see whether a relationship exists between the outside temperature and the number of emergency calls it receives for a 7-hour period. The data are shown. Temperature x No. of calls y 68 74 7 4 8 82 88 10 93 11 99 9 Test the significance of the correlation coefficient at alpha = 0.05 13 101 f = Step 1: State the hypotheses. Step 2: Find the critical values. Step 3. Compute the test value. Step 4. Make the decision. Step 5. Summarize the results.The scale of the correlation coefficient is: a. nominal b. ordinal c. ratioFor the data given in the table below, find the linear correlation coefficient r and the least-squares regression line x y ------- 1 18 3 13 3 9 6 6 7 4 -------
- Here is a bivariate data set. x y -1 78 -27 214 39 -43 19 -3 -9 88 -3 66 25 64 Find the correlation coefficient and report it accurate to four decimal places.r = A good correlation calculator is found at Correlation CalculatorQQ3. Diamond PricesWeight 0.3 0.4 0.5 0.5 1.0 0.7Price 510 1151 1343 1410 5669 2277Find the best predicted price for this diamond with a weight of 1.50 carats. Is the result close tothe actual price of $16,097? What is wrong with predicting the price of a 1.50-carat diamond? a) Find the value of the linear correlation coefficient ?b) Find the critical values of r from table A-6 using ∝= 0.05c) Determine whether there is sufficient evidence to support a claim of a linear correlationBetween the two variables.The grades of a class of 9 students on a midterm report (x) and on the final examination (y) are as follows: Give the following: a. linear regression line and equation b. computation of the coefficient of determination ?^2 c. Computation of the coefficient of correlation ? d. Estimate the final examination grade of a student who received a grade of 85 on the midterm report.