 # Confidence intervals questions and answers

Recent questions in Confidence intervals vestirme4 2021-09-18 Answered

### In a survey of 2695 adults, 1446 say they have started paying bills online in the last year. Construct a $$\displaystyle{99}\%$$ confidence interval for the population proportion. Interpret your results. Choose the correct answer below. A) With $$\displaystyle{95}\%$$ confidence, it can be said that the sample proportion of adults who say they have started paying bills online in the last year is between the endpoints of the given confidence interval B) With $$\displaystyle{99}\%$$ confidence, it can be said that the population proportion of adults who say they have started paying bills online in the last year is between the endpoints of the given confidence interval. C) The endpoints of the given confidence interval show that adults pay bills online $$\displaystyle{99}\%$$ of the time. opatovaL 2021-09-18 Answered

### A standard normal table, also called the unit normal table or Z table, may be a mathematical table for the values of $$\displaystyle\phi$$, which are the values of the cumulative distribution function of the traditional distribution. $$\begin{array}{|c|c|}\hline \text{confidence intervals} & Z \\ \hline 90 & 1.645 \\ \hline 95 & 1.96 \\ \hline 96 & 2.05 \\ \hline 97 & 2.17 \\ \hline 98 & 2.326 \\ \hline 99 & 2.576 \\ \hline \end{array}$$ a) How do calculate Z-score using the confidence interval? floymdiT 2021-09-18 Answered

### 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. $$\begin{array}{|c|c|}\hline 775 & 773 & 807 & 797 & 791 & 769 & 789 & 768 & 805 & 763 & 771 & 792 \\ \hline \end{array}$$ midtlinjeg 2021-09-17 Answered

### $$\begin{array}{|c|c|} \hline 25.6&23.8&26.5&23.9&24.8 \\ \hline 24.7&20.9&26&22.2&27 \\ \hline \end{array}$$ What Equation to use to construct a $$\displaystyle{99}\%$$ lower confidence bound for $$\displaystyle\sigma^{{{2}}}$$ Isa Trevino 2021-09-17 Answered

### A set of data consists of 45 observations between 0 and 29. What size would you recommend for the class interval? ka1leE 2021-09-16 Answered

### A random sample of 820 households from a city, Stats City, were surveyed. From the statistical technology, we find a $$\displaystyle{95}\%$$ confidence interval for the mean number of people in the households was $$\displaystyle{1.85}{<}\mu{<}{3.25}$$ What is the true meaning of the interval presented in the problem about Stats City? babeeb0oL 2021-09-16 Answered

### A survey of several 10 to 11 year olds recorded the following amounts spent on a trip to the mall: $19.17,$21.18,$20.38,$25.08 Construct the $$\displaystyle{90}\%$$ confidence interval for the average amount spent by 10 to 11 year olds on a trip to the mall. Assume the population is approximately normal. Copy Data Step 4 of 4 : Construct the $$\displaystyle{90}\%$$ confidence interval. Round your answer to two decimal places. glamrockqueen7 2021-09-16 Answered

### Express the confidence interval $$57.7 \% \pm 4.9 \%$$ in interval form. Express the answer in decimal format (donot eter as percents). Khaleesi Herbert 2021-09-15 Answered

### Use the Intermediate Value Theorem to show that there is a root of the given equation in the specified interval. $$\displaystyle{x}^{{{4}}}+{x}-{3}={0},$$ (1,2) ddaeeric 2021-09-15 Answered

### How do you solve? A healthcare provider monitors the number of CAT scans performed each month in each of its clinics. The most recent year of data for a particular clinics follows (the reported variable is the number of CAT scans each month expressed as the number of CAT scans per thousand members of the health plan): 2.31,2.09,2.36,1.95,1.98,2.25,2.16,2.07,1.88,1.94,1.97,2.02. Find a two-sided $$\displaystyle{95}\%$$ confidence interval for the standard deviation. What should you do to address any reservations about this confidence interval? Round your answers to two decimal places (e.g. 98.76). $$\displaystyle\leq\sigma\leq$$ sagnuhh 2021-08-14 Answered

### When σ is unknown and the sample size is $$\displaystyle{n}\geq{30}$$, there are tow methods for computing confidence intervals for μμ. Method 1: Use the Student's t distribution with d.f. = n - 1. This is the method used in the text. It is widely employed in statistical studies. Also, most statistical software packages use this method. Method 2: When $$\displaystyle{n}\geq{30}$$, use the sample standard deviation s as an estimate for σσ, and then use the standard normal distribution. This method is based on the fact that for large samples, s is a fairly good approximation for σσ. Also, for large n, the critical values for the Student's t distribution approach those of the standard normal distribution. Consider a random sample of size n = 31, with sample mean x¯=45.2 and sample standard deviation s = 5.3. (c) Compare intervals for the two methods. Would you say that confidence intervals using a Student's t distribution are more conservative in the sense that they tend to be longer than intervals based on the standard normal distribution? Isa Trevino 2021-08-14 Answered

### You are interested in finding a $$\displaystyle{95}\%$$ confidence interval for the mean number of visits for physical therapy patients. The data below show the number of visits for 14 randomly selected physical therapy patients. Round answers to 3 decimal places where possible. $$\begin{array}{|c|c|}\hline 9 & 6 & 10 & 15 & 19 & 6 & 23 & 26 & 19 & 16 & 11 & 25 & 16 & 11 \\ \hline \end{array}$$ a) To compute the confidence interval use a t or z distribution. b) With $$\displaystyle{95}\%$$ confidence the population mean number of visits per physical therapy patient is between "?" and "?" visits. c) If many groups of 14 randomly selected physical therapy patients are studied, then a different confidence interval would be produced from each group. About "?" percent of these confidence intervals will contain the true population mean number of visits per patient and about "?" percent will not contain the true population mean number of visits per patient. Anish Buchanan 2021-08-12 Answered

### When σ is unknown and the sample size is $$\displaystyle{n}\geq{30}$$, there are tow methods for computing confidence intervals for μμ. Method 1: Use the Student's t distribution with d.f. = n - 1. This is the method used in the text. It is widely employed in statistical studies. Also, most statistical software packages use this method. Method 2: When $$\displaystyle{n}\geq{30}$$, use the sample standard deviation s as an estimate for σσ, and then use the standard normal distribution. This method is based on the fact that for large samples, s is a fairly good approximation for σσ. Also, for large n, the critical values for the Student's t distribution approach those of the standard normal distribution. Consider a random sample of size n = 31, with sample mean x¯=45.2 and sample standard deviation s = 5.3. (c) Compare intervals for the two methods. Would you say that confidence intervals using a Student's t distribution are more conservative in the sense that they tend to be longer than intervals based on the standard normal distribution? waigaK 2021-08-12 Answered

### In a science fair​ project, Emily conducted an experiment in which she tested professional touch therapists to see if they could sense her energy field. She flipped a coin to select either her right hand or her left​ hand, and then she asked the therapists to identify the selected hand by placing their hand just under​ Emily's hand without seeing it and without touching it. Among 358 ​trials, the touch therapists were correct 172 times. Complete parts​ (a) through​ (d). a) Given that Emily used a coin toss to select either her right hand or her left​ hand, what proportion of correct responses would be expected if the touch therapists made random​ guesses? ​(Type an integer or a decimal. Do not​ round.) b) Using​ Emily's sample​ results, what is the best point estimate of the​ therapists' success​ rate? ​(Round to three decimal places as​ needed.) c) Using​ Emily's sample​ results, construct a $$\displaystyle{90}​\%$$ confidence interval estimate of the proportion of correct responses made by touch therapists. Round to three decimal places as​ needed - ?$$\displaystyle{<}{p}{<}$$? iohanetc 2021-08-10 Answered

### Is there a relationship between confidence intervals and two-tailed hypothesis tests? Let e be the level of confidence used to construct a confidence interval from sample data. Let αα be the level of significance for a two-tailed hypothesis test. The following statement applies to hypothesis tests of the mean. (A corresponding relationship between confidence intervals and two-tailed hypothesis tests also is valid for other parameters such as p, '$$\mu_{1}-\mu_{2}$$, or $$p_{1}-p_{2}$$, which we will study in Section 9.3, 10.2, and 10.3.) Whenever the value of k given in the null hypothesis falls outside the c=1−α confidence interval for the parameter, we reject $$H_{0}$$. For example, consider a two-tailed hypothesis test with \alpha =0.01 and $$H_{0}:\mu =20 H_{1}:\mu 20$$ sample mean x¯=22 from a population with standard deviation σ=4. (a) What is the value of c=1−α. Using the methods, construct a 1−α confidence interval for μ from the sample data. What is the value of μ given in the null hypothesis (i.e., what is k)? Is this value in the confidence interval? Do we reject or fail to reject H0 based on this information? (b) using methods, find the P-value for the hypothesis test. Do we reject or fail to reject $$H_0$$? Compare your result to that of part (a). Brittney Lord 2021-08-10 Answered

### ACTIVITY H: Sampling Theory and Estimation of Parameters 1. A random sample of 50 students in Holy Angel University shows that they spend an average of 3 hours per day on social media apps with a standard deviation of 0.5 hours. Assume a normal distribution. Construct a $$\displaystyle{90}\%$$ and $$\displaystyle{97}\%$$ confidence interval for the average number of hours spent on social media apps per day. 2. A study was conducted in which two types of fried chicken, Jollibee and KFC, were compared. Number of fried chickens sold, was measured. 90 Jollibee branches were surveyed while 80 were surveyed for KFC. The average fried chicken sold was 7,020 for Jollibee and 8,100 fried chickens for KFC. Find a $$\displaystyle{94}\%$$ and $$\displaystyle{98}\%$$ confidence interval on .Assume that the population standard deviations are 1000 and 500 for KFC and ????--?????????Jollibee, respectively. 3. The following are the average lengths of today’s top 10 Global Spotify hits, in minutes. 3.02, 2.85, 3.33, 3.43, 2.9, 2.93, 3.23, 2.77, 2.45, and 2.88. Find a $$\displaystyle{95}\%$$ confidence interval for the variance of the lengths of this generation’s music, assuming a normal population. UkusakazaL 2021-08-10

### Consider the following data set below. Find the UPPER INTERVAL of the population mean at $$\displaystyle{80}\%$$ confidence interval. (write your answer in two decimal places) Given: 12,10,9,11 UkusakazaL 2021-08-10 Answered

### Use the confidence interval to find the margin of error and the sample mean. (0.142, 0.300) The margin of error is ?. The sample mean is ?. UkusakazaL 2021-08-10 Answered

### The high price of medicines is a source of major expense for those seniors in the United States who have to pay for these medicines themselves. A random sample of 2000 seniors who pay for their medicines showed that they spent an average of $$\displaystyle\{4600}$$ last year on medicines with a standard deviation of $$\displaystyle\{800}$$. a) Make a $$\displaystyle{98}\%$$ confidence interval for the corresponding population mean. b) Suppose the confidence interval obtained in part a is too wide. How can the width of this interval be reduced? Discuss allpossible alternatives. Which alternative is the best? UkusakazaL 2021-08-10

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