A new catalyst is being investigated for use in the production of a plastic chemical. Ten batches of the chemical are produced. The mean yield of the 10 batches is 72.5% and the standard deviation is 5.8%. Assume the yields are independent and approximately normally distributed. Find a 99% conﬁdence interval for the mean yield when the new catalyst is used.Q1: 12 (Exercise for Section 5.2)In a random sample of 150 customers of a high-speed internet provider, 63 said that their service had been interrupted one or more times in the past month.Find a 95% conﬁdence interval for the proportion of customers whose service was interrupted one or more times in the past month.Find a 99% conﬁdence interval for the proportion of customers whose service was interrupted one or more times in the past month.Find the sample size needed for a 95% conﬁdence interval to specify the proportion to within ± 0.05Find the sample size needed for a 99% conﬁdence interval to specify the proportion to within±0.05.Do bathroom scales tend to underestimate a person’s true weight? A 150 lb test weight was placed on each of 50 bathrooms scales. The readings on 29 of the scales were too light, and the readings on the other 21 were too heavy. Can you conclude that more than half of bathroom scales underestimate weight?A broth used to manufacture a pharmaceutical product has its sugar contents, in mg/mL ,measured several times on each of three successive days.Day 1: 5.0 4.8 5.1 5.1 4.8 5.1 4.8 4.8 5.0 5.2 4.9 4.9 5.0 Day 2: 5.8 4.7 4.7 4.9 5.1 4.9 5.4 5.3 5.3 4.8 5.7 5.1 5.7Day 3: 6.3 4.7 5.1 5.9 5.1 5.9 4.7 6.0 5.3 4.9 5.7 5.3 5.6Can you conclude that the variability of the process is greater on the second day than on the ﬁrst day?Can you conclude that the variability of the process is greater on the third day than on the second day?Mom and Grandma are each baking chocolate chip cookies. Each gives you two cookies. One of Mom’s cookies has 14 chips in it and the other has 11. Grandma’s cookies have 6 and 8 chips.Estimate the mean number of chips in one of Mom’s cookies.Estimate the mean number of chips in one of Grandma’s cookies.Find the uncertainty in the estimate for Mom’s cookies.Find the uncertainty in the estimate for Grandma’s cookies.Estimate how many more chips there are on the average in one of Mom’s cookies than in one of Grandma’s. Find the uncertainty in this estimate.

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MATLAB: An Introduction with Applications

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ISBN:9781119256830

Author:Amos Gilat

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A new catalyst is being investigated for use in the production of a plastic chemical. Ten batches of the chemical are produced. The mean yield of the 10 batches is 72.5% and the standard deviation is 5.8%. Assume the yields are independent and approximately normally distributed. Find a 99% conﬁdence interval for the mean yield when the new catalyst is used.
Q1: 12 (Exercise for Section 5.2)
1. In a random sample of 150 customers of a high-speed internet provider, 63 said that their service had been interrupted one or more times in the past month.
2. Find a 95% conﬁdence interval for the proportion of customers whose service was interrupted one or more times in the past month.
3. Find a 99% conﬁdence interval for the proportion of customers whose service was interrupted one or more times in the past month.
4. Find the sample size needed for a 95% conﬁdence interval to specify the proportion to within ± 0.05
5. Find the sample size needed for a 99% conﬁdence interval to specify the proportion to within±0.05.
Do bathroom scales tend to underestimate a person’s true weight? A 150 lb test weight was placed on each of 50 bathrooms scales. The readings on 29 of the scales were too light, and the readings on the other 21 were too heavy. Can you conclude that more than half of bathroom scales underestimate weight?
1. A broth used to manufacture a pharmaceutical product has its sugar contents, in mg/mL ,measured several times on each of three successive days.
Day 1: 5.0 4.8 5.1 5.1 4.8 5.1 4.8 4.8 5.0 5.2 4.9 4.9 5.0

Day 2: 5.8 4.7 4.7 4.9 5.1 4.9 5.4 5.3 5.3 4.8 5.7 5.1 5.7

Day 3: 6.3 4.7 5.1 5.9 5.1 5.9 4.7 6.0 5.3 4.9 5.7 5.3 5.6
1. Can you conclude that the variability of the process is greater on the second day than on the ﬁrst day?
2. Can you conclude that the variability of the process is greater on the third day than on the second day?
Mom and Grandma are each baking chocolate chip cookies. Each gives you two cookies. One of Mom’s cookies has 14 chips in it and the other has 11. Grandma’s cookies have 6 and 8 chips.
Estimate the mean number of chips in one of Mom’s cookies.
Estimate the mean number of chips in one of Grandma’s cookies.
Find the uncertainty in the estimate for Mom’s cookies.
Find the uncertainty in the estimate for Grandma’s cookies.
Estimate how many more chips there are on the average in one of Mom’s cookies than in one of Grandma’s. Find the uncertainty in this estimate.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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