A regression of x = tannin concentration (mg/L) and y = perceived astringency score was considered in Examples 5.2 and 5.6. The perceived astringency was computed from expert tasters rating a wine on a scale from 0 to 10 and then standardizing the rating by computing a z-score. Data for 32 red wines (given in Example 5.2) was used to compute the following summary statistics and estimated regression line:

a. Calculate a 95% confidence interval for the mean astringency rating for red wines with a tannin concentration of .5 mg/L.
b. When two 95% confidence intervals are computed, it can be shown that the simultaneous confidence level is at least 3100 2 2152 4% = 90%. That is, if both intervals are computed for a first sample, for a second sample, for a third sample, and so on, in the long run at least 90% of the samples will result in intervals which both capture the values of the corresponding population characteristics. Calculate confidence intervals for the mean astringency rating when the tannin concentration is .5 mg/L and when the tannin concentration is .7 mg/L in such a way that the simultaneous confidence level is at least 90%.
c. If two 99% confidence intervals were computed, what do you think could be said about the simultaneous confidence level?
d. If a 95% confidence interval were computed for the mean astringency rating when x = .5, another confidence interval was computed for x = .6, and yet another one for x = .7, what do you think would be the simultaneous confidence level for the three resulting intervals?

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n-32 SSResid x=.6069 Σ (x_x)-1.479 1.936 y =-1.59 + 2.59x