# Confidence intervals questions and answers

Recent questions in Confidence intervals

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

Isa Trevino 2021-09-17 Answered

### 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

### 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

### 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