 # Confidence intervals questions and answers

Recent questions in Confidence intervals UkusakazaL 2021-08-10

### To monitor complex chemical processes, chemical engineers will consider key process indicators, which may be just yield but most often depend on several quantities. Before trying to improve a process, 9 measurements were made on a key performance indicator. 123, 106, 114, 128, 113, 109, 120, 102, 111. Assume that the key performance indicator has a normal distribution. (a) Find the sample variance s 2 of the sample. (b) Find a $$\displaystyle{95}\%$$ confidence interval for $$\displaystyle\sigma{2}$$. (c) Find a $$\displaystyle{98}\%$$ confidence interval for $$\displaystyle\sigma$$. UkusakazaL 2021-08-10

### A local firm manufactures LED products that have a lifespan that is approximately normally distributed with a std. dev. of 30 hours. If a sample of 30 LED products has an average lifespan of 780 hours, find a $$\displaystyle{96}\%$$ confidence interval for the population mean of all LED products produced by this firm. Choose 2 answers in nearest unit (ones) or in whole number. Example, if your answer is $$\displaystyle{888.83}\leq\mu\leq{899.56}$$, choose 889 and 900. $$\begin{array}{|c|c|}\hline 775 & 773 & 807 & 797 & 791 & 769 & 789 & 768 & 805 & 763 & 771 & 792 \\ \hline \end{array}$$ UkusakazaL 2021-08-10

### Out of 200 people sampled, 116 preferred Candidate A. Based on this, estimate what proportion of the voting population prefers Candidate A with $$\displaystyle{99}\%$$ confidence. Out of 500 people sampled, 455 had kids. The best point estimate for pp is. The margin of error for a $$\displaystyle{99}\%$$ confidence interval is. Sinead Mcgee 2021-08-09 Answered

### A clinical trial was conducted to test the effectiveness of a drug for treating insomnia in older subjects. Before​ treatment, 13 subjects had a mean wake time of 101.0 min. After​ treatment, the 13 subjects had a mean wake time of 94.6 min and a standard deviation of 24.9 min. Assume that the 13 sample values appear to be from a normally distributed population and construct a $$\displaystyle{95}​\%$$ confidence interval estimate of the mean wake time for a population with drug treatments. What does the result suggest about the mean wake time of 101.0 min before the​ treatment? Does the drug appear to be​ effective? Construct the $$\displaystyle{95}​\%$$ confidence interval estimate of the mean wake time for a population with the treatment. $$\min{<}\mu<\min$$ ​(Round to one decimal place as​ needed.) What does the result suggest about the mean wake time of 101.0 min before the​ treatment? Does the drug appear to be​ effective? The confidence interval ▼ does not include| includes the mean wake time of 101.0 min before the​ treatment, so the means before and after the treatment ▼ could be the same |are different. This result suggests that the drug treatment ▼ does not have | has a significant effect. UkusakazaL 2021-08-09

### Customers randomly selected at a grocery store included 172 women and 45 men. 74 of the women and 12 of the men used coupons. Find the $$\displaystyle{95}\%$$ confidence interval. UkusakazaL 2021-08-09

### Unoccupied seats on flights cause airlines to lose revenue. Suppose a large airline wants to estimate its average number of unoccupied seats per flight over the past year. To accomplish this, the records of 200 flights are randomly selected and the number of unoccupied seats is noted for each of the sampled flights. The sample mean is 11.6 seats and the sample standard deviation is 4.3 seats. $$\displaystyle{s}_{{{x}}}=?,\ {n}=?,\ {n}-{1}=?$$. Construct a $$\displaystyle{92}\%$$ confidence interval for the population average number of unoccupied seats per flight. (State the confidence interval. (Round your answers to two decimal places.) UkusakazaL 2021-08-09

### Your client from question 4 decides they want a $$\displaystyle{90}\%$$ confidence interval instead of a $$\displaystyle{95}\%$$ one. To remind you - you sampled 36 students to find out how many hours they spent online last week. Your sample mean is 46. The population standard deviation, $$\displaystyle\sigma$$, is 7.4. What is the $$\displaystyle{90}\%$$ confidence interval for this sample mean? Keep at least three decimal places on any intermediate calculations, then give your answer rounded to 1 decimal place, with the lower end first then upper. (_______ , ___________ ) UkusakazaL 2021-08-09

### The scores of a certain population on the Wechsler Intelligence Scale for children (WISC) are thought to be normally distributed with a mean and standard deviation of 10. A simple random sample of twenty -five children from this population is taken and each is given the WISC. The mean of the twenty-five score is $$\displaystyle\overline{{{x}}}={104.32}$$. Based on these data a $$\displaystyle{95}\%$$ confidence interval for $$\displaystyle\mu$$ is computed. The $$\displaystyle{95}\%$$ confidence interval for $$\displaystyle\mu$$ is? UkusakazaL 2021-08-09

### Confidence Intervals. In Exercises 9–24, construct the confidence interval estimate of the mean. Genes Samples of DNA are collected, and the four DNA bases of A, G, C, and T are coded as 1, 2, 3, and 4, respectively. The results are listed below. Construct a 95% confidence interval estimate of the mean. What is the practical use of the confidence interval? 2 2 1 4 3 3 3 3 4 1 Wribreeminsl 2021-08-08 Answered

### A clinical trial was conducted to test the effectiveness of a drug for treating insomnia in older subjects. Before treatment, 24 subjects had a mean wake time of 104.0 min. After treatment, the 24 subjects had a mean wake time of 94.5 min and a standard deviation of 23.2 min. Assume that the 24 sample values appear to be from a normally distributed population and construct a $$\displaystyle{99}\%$$ confidence interval estimate of the mean wake time for a population with drug treatments. What does the result suggest about the mean wake time of 104.0 min before the treatment? Does the drug appear to be effective? Construct the $$\displaystyle{99}\%$$ confidence interval estimate of the mean wake time for a population with the treatment. $$\displaystyle?\min{<}\mu{<}?\min$$ UkusakazaL 2021-08-08

### Survey A asked 1000 people how they liked the new movie Avengers: Endgame and $$\displaystyle{88}\%$$ said they did enjoy it. Survey B also concluded that $$\displaystyle{82}\%$$ of people liked the move but they asked 1600 total moviegoers. Which of the following is true about this comparison? The margin of error is the same for both. The confidence interval is smaller for Survey B. Increasing the number of people asked does not change the $$\displaystyle{95}\%$$ confidence interval. Survey A is more accurate since the percentage is higher. Survey A has more approvals than Survey B. Survey A is better than Survey B since it has a higher percentage. UkusakazaL 2021-08-08

### a. Locate the critical points of ƒ. b. Use the First Derivative Test to locate the local maximum and minimum values. c. Identify the absolute maximum and minimum values of the function on the given interval (when they exist). $$\displaystyle{f{{\left({x}\right)}}}={\frac{{{x}^{{{2}}}}}{{{x}^{{{2}}}-{1}}}}$$ on $$\displaystyle{\left[-{4},{4}\right]}$$ UkusakazaL 2021-08-08

### Explain what is the test statistic used for constructing confidence interval on a proportion. UkusakazaL 2021-08-08

### Based on a simple random sample of 1300 college students, it is found that 299 students own a car. We wish to construct a $$\displaystyle{90}\%$$ confidence interval to estimate the proportions ? of all college students who own a car. A) Read carefully the text and provide each of the following: The sample size $$\displaystyle?=$$ from the sample, the number of college students who own a car is $$\displaystyle?=$$ the confidence level is $$\displaystyle{C}{L}=$$ $$\displaystyle\%$$. B) Find the sample proportion $$\displaystyle\hat{{?}}=$$ and $$\displaystyle\hat{{?}}={1}−\hat{{?}}=$$ UkusakazaL 2021-08-08 Answered

### We walk from Central Park to Empire State Building with a constant speed. Our speed X is a random variable uniformly distributed between 3 and 4.5 km/h. The distance is 3 km. Calculate the probability distribution of the total walking time T: a. Calculate the CDF of T from the distribution of X. b. Calculate the PDF of T from irs CDF. Don't forget to specify the intervals for these functions explicitly. UkusakazaL 2021-08-08 Answered

### Express the confidence interval $$\displaystyle{\left({0.412},\ {0.789}\right)}$$ in the form of $$\displaystyle\hat{{{p}}}\pm{E}$$. UkusakazaL 2021-08-08 Answered

### From a simple random sample of 14 shoppers surveyed, the sample mean of money spent for holiday gifts was 145 dollars with a sample standard deviation of 11 dollars. We wish to construct a $$\displaystyle{99}\%$$ confidence interval for the population mean of money spent for holiday gifts. Read carefully the text and provide each of the following: The sample size $$\displaystyle?=$$, the sample mean $$\displaystyle?\equiv$$, the sample standard deviation $$\displaystyle?=$$, NKS the confidence level $$\displaystyle{C}{L}=\%$$. UkusakazaL 2021-08-08

### Assume that the true value, that is the population mean, the average height of french women in france is 167.5 cm. Students in a class of 160 students each took a random sample of french women of size 100, measured the height of the women and calculated a 95% confidence interval (confidence interval) for the average height.How many students can be expected to calculate a confidence interval that does not include the number 167.5? 15 8 5 20 1 smileycellist2 2021-08-07 Answered

### A salesperson goes door-to-door in a residential area to demonstrate the use of a new household appliance to potential customers. At the end of a demonstration,the probability that the potential customer would place an order for the product is aconstant 0.2107. To perform satisfactorily on the job, the salesperson needs at leastfour orders. Assume that each demonstration is a Bernoulli trial. a. If the salesperson wants to be at least $$\displaystyle{90}\%$$ confident of getting at least 4 orders, at least how many demonstrations should she make? b. The salesperson has time to make only 22 demonstrations, and she still wants to be at least $$\displaystyle{90}\%$$ confident of getting at least 4 orders. She intends to gain this confidence by improving the quality of her demonstration and thereby improving the chances of getting an order at the end of a demonstration. At least to what value should this probability be increased in order to gain the desired confidence? Your answer should be accurate to four decimal places. naivlingr 2021-08-07 Answered

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