14.5 please! ...95% for u: or (100.56, 111.12)CONFIDENCE INTERVALS FOR THE MEAN u0806OLIQ scoresOL120130CURE 14.4 Dotplot of thne la scores of 31 seventh-grade girls.. Check the conditions for inference. Here are the “simple conditions":PS: The girls are an SRS from the population of all seventh-grade girls inthe school district.lues that are typically rounded to the nearest integer when provided. WeeYpect from experience that IQ scores in a homogeneous population withsimilar developmental age will follow approximately a Normal distribution.We can't look at the population, but we can examine the sample. Figure 14.4shows a dotplot of the data. Its shape is slightly left-skewed, but there are noextreme outliers. Thus, we have no reason to doubt that the population dis-Tribution is close to Normal. Additionally, the central limit theorem tells usthat a sample size of 31 is large enough to overcome moderate departures fromNormality for performing inference.STE AEXVN3. Known o: Most IQ tests are designed so that o = 15, so it is not unrealisticto assume that we know that o = 15 for our calculations.SOLVE: Obtain the confidence interval. Using statistical software and inputtingthe raw data, we obtain a 95% confidence interval of (100.56, 111.12) for themean IQ score u in this population.CONCLUDE: We are 95% confident that the mean IQ score for all seventh-gradegirls in this Midwest school district is between 100.6 and 111.1.The computations performed by any statistical software in this example involvethe following steps:Sample mean: I = 105.84Critical value for a 95% confidence level: 2* =1.960%3DMargin of error: m = 2* o//n= (1.96)(15)//31 =5.28%3D* 5% confidence interval for u:±m=105.84 ±5.28, or (100.56, 111.12)n thir introductory chapter, we work with examples for which the "simpledlu inference methods are often APPLY YOUR KNOWLEDGE14.4 Critical value and confidence level. This section provided the Normal crieical values z* for three commonly used confidence levels (90%, 95%, and 99%)Explain briefly why the critical value must be larger for a larger confidence level14.5 Pharmaceutical production. A manufacturer of pharmaceutical products ana-lyzes each batch of a product to verify the concentration of the active ingredient.The chemical analysis is not perfectly precise. In fact, repeated measurementsfollow a Normal distribution with mean u equal to the true concentration andwith standard deviation o = 0.0068 grams per liter (g/l). Three analyses of onebatch give concentrations of 0.8403, 0.8363, and 0.8447 g/l. To estimate the trueconcentration, give a 95% confidence interval for u. Follow the four-step processas illustrated in Example 14.3.loordbabshHYPOTHESIS TESTINGConfidence intervals are one of the two most common types of statistical infeence. Use a confidence interval when your goal is to estimate a population parareter. Another common type of inference, called hypothesis tests (or sometim

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14.5 please! ...95% for u: or (100.56, 111.12)CONFIDENCE INTERVALS FOR THE MEAN u0806OLIQ scoresOL120130CURE 14.4 Dotplot of thne la scores of 31 seventh-grade girls.. Check the conditions for inference. Here are the “simple conditions&#34;:PS: The girls are an SRS from the population of all seventh-grade girls inthe school district.lues that are typically rounded to the nearest integer when provided. WeeYpect from experience that IQ scores in a homogeneous population withsimilar developmental age will follow approximately a Normal distribution.We can't look at the population, but we can examine the sample. Figure 14.4shows a dotplot of the data. Its shape is slightly left-skewed, but there are noextreme outliers. Thus, we have no reason to doubt that the population dis-Tribution is close to Normal. Additionally, the central limit theorem tells usthat a sample size of 31 is large enough to overcome moderate departures fromNormality for performing inference.STE AEXVN3. Known o: Most IQ tests are designed so that o = 15, so it is not unrealisticto assume that we know that o = 15 for our calculations.SOLVE: Obtain the confidence interval. Using statistical software and inputtingthe raw data, we obtain a 95% confidence interval of (100.56, 111.12) for themean IQ score u in this population.CONCLUDE: We are 95% confident that the mean IQ score for all seventh-gradegirls in this Midwest school district is between 100.6 and 111.1.The computations performed by any statistical software in this example involvethe following steps:Sample mean: I = 105.84Critical value for a 95% confidence level: 2* =1.960%3DMargin of error: m = 2* o//n= (1.96)(15)//31 =5.28%3D* 5% confidence interval for u:±m=105.84 ±5.28, or (100.56, 111.12)n thir introductory chapter, we work with examples for which the &#34;simpledlu inference methods are often APPLY YOUR KNOWLEDGE14.4 Critical value and confidence level. This section provided the Normal crieical values z* for three commonly used confidence levels (90%, 95%, and 99%)Explain briefly why the critical value must be larger for a larger confidence level14.5 Pharmaceutical production. A manufacturer of pharmaceutical products ana-lyzes each batch of a product to verify the concentration of the active ingredient.The chemical analysis is not perfectly precise. In fact, repeated measurementsfollow a Normal distribution with mean u equal to the true concentration andwith standard deviation o = 0.0068 grams per liter (g/l). Three analyses of onebatch give concentrations of 0.8403, 0.8363, and 0.8447 g/l. To estimate the trueconcentration, give a 95% confidence interval for u. Follow the four-step processas illustrated in Example 14.3.loordbabshHYPOTHESIS TESTINGConfidence intervals are one of the two most common types of statistical infeence. Use a confidence interval when your goal is to estimate a population parareter. Another common type of inference, called hypothesis tests (or sometim

Accepted Answer

Solution:
Let X be the concentration.
The given data for X is 0.8403, 0.8363 and 0.8447.