**Constructing a Confidence Interval**Assume that we want to construct a confidence interval. You have the following options, as appropriate:(a) Find the critical value \( t_{\alpha/2} \).(b) Find the critical value \( z_{\alpha/2} \).(c) State if neither the normal distribution nor the t distribution applies.Here are the summary statistics for randomly selected weights of newborn girls:- \( n = 226 \)- \( \bar{x} = 31.8 \) hg- \( s = 7.5 \) hgThe confidence level is 95%.---**Explanation:**In statistics, constructing a confidence interval involves determining the range in which we expect a population parameter to lie. Here, you can decide whether to use the t-distribution or z-distribution based on the given sample size and other criteria. 1. **\( t_{\alpha/2} \) Critical Value:** - Used when the sample size is small (typically \( n < 30 \)) or the population standard deviation is unknown. - Appropriate for this example depending on the nature of the population distribution.2. **\( z_{\alpha/2} \) Critical Value:** - Used when the sample size is large (typically \( n \geq 30 \)) and the population standard deviation is known or the sample is drawn from a normally distributed population. - Appropriate here since the sample size is large (\( n = 226 \)).3. **Decision on Distributions:** - Assess if the assumptions for normal or t distributions are met. If not, indicate the inapplicability of both.This process helps in making inferences about the population with a specified level of confidence, here given as 95%.

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Assume that we want to construct a confidence interval. Do one of the following, as appropriate: (a) find the critical value tα/2, (b) find the critical value zα/2, or (c) state that neither the normal distribution nor the t distribution applies. The confidence level is 95%, σ is not known, and the histogram of 61 player salaries (in thousands of dollars) of football players on a team is as shown. 040008000120001600020000010203040Salary (thousands of dollars)Frequency A histogram has a horizontal axis labeled "Salary (thousands of dollars)" from below 0 to above 20000 in increments of 2000 and a vertical axis labeled "Frequency" from 0 to 40 in increments of 10. The histogram contains vertical bars of width 2000, where one vertical bar is centered over each of the horizontal axis tick marks. The heights of the vertical bars are as follows, where the salary is listed first and the height is listed second: 0, 34; 2000, 16; 4000,…
A statistics class is estimating the mean height of all female students at their college. They collect a random sample of 42 female students and measure their heights. The mean of the sample is 65.3 inches and the sample standard deviation is 5.4 inches. Find the 90% confidence interval for the mean height of all female students in their school? Assume that the distribution of individual female heights at this school is approximately normal. 1. The t value is 1.3025 2. The standard error has a value of -- 3. The margin of error has a value of 4. Find the 90% confidence interval for the mean height of all female students in their school
Assume that we want to construct a confidence interval. Do one of the following, as appropriate. (a) Find the critical value zα/2, (b) find the critical value tα/2, or (c) state that neither the normal nor the t distribution applies. Confidence level is 95%, σ=23.5, and the histogram of right-eye vision mea surements from a random sample of 52 adult males is shown to the right. 05010015020001020304050Vision in Right EyeFrequency A histogram has a horizontal axis labeled "Vision in Right Eye" from 0 to greater than 200 in increments of 25 and a vertical axis labeled Frequency from 0 to 50 in increments of 10. The histogram contains vertical bars of width 25, where each vertical bar is centered over a horizontal axis tick mark. The heights of the three vertical bars are as follows, where the horizontal axis value is listed first and the height is listed second: 25, 37; 50, 14; 200, 1. Select the correct choice below and,…
Assume that we want to construct a confidence interval. Do one of the following, as appropriate: (a) find the critical value to/2, (b) find the critical value Zα/2, or (c) state that neither the normal distribution nor the t distribution applies. Here are summary statistics for randomly selected weights of newborn girls: n = 286, x = 33.3 hg, s = 6.4 hg. The confidence level is 95%. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. ta/2= B. (Round to two decimal places as needed.) Za/2 = (Round to two decimal places as needed.) C. Neither the normal distribution nor the t distribution applies.
Assume that we want to construct a confidence interval. Do one of the following, as appropriate: (a) find the critical value tα/2, (b) find the critical value zα/2, or (c) state that neither the normal distribution nor the t distribution applies. Here are summary statistics for randomly selected weights of newborn girls: n=236, x=31.6 hg, s=6.9 hg. The confidence level is 90%.
Assume that we want to construct a confidence interval. Do one of the following, as appropriate: (a) find the critical value t/2, (b) find the critical value z,/2, or (c) state that neither the normal distribution nor the t distribution applies. 230, x 32.6 hg, s = 7.9 hg. The confidence level is 90% Here are summary statistics for randomly selected weights of newborn girls: n Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. (Round to two decimal places as needed.) В. Za/2 (Round to two decimal places as needed.) C. Neither the normal distribution nor the t distribution applies.
Assume that we want to construct a confidence interval. Do one of the following, as appropriate: (a) find the critical value to/2, (b) find the critical value Za/2, or (c) state that neither the normal distribution nor the t distribution applies. Here are summary statistics for randomly selected weights of newborn girls: n=287, x= 29.9 hg, s= 6.8 hg. The confidence level is 90%. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. ta/2= OB. (Round to two decimal places as needed.) Zα/2 (Round to two decimal places as needed.) OC. Neither the normal distribution nor the t distribution applies.
Assume that we want to construct a confidence interval. Do one of the following, as appropriate: (a) find the critical value ty/2, (b) find the critical value za12, or (c) state that neither the normal distribution nor the t distribution applies. Here are summary statistics for randomly selected weights of newborn girls: n= 293, x= 33.5 hg, s= 7.2 hg. The confidence level is 99%. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. ta/2= %3D (Round to two decimal places as needed.) В. Za/2 = (Round to two decimal places as needed.) C. Neither the normal distribution nor the t distribution applies.
Assume that we want to construct a confidence interval. Do one of the following, as appropriate: (a) find the critical value t/2. (b) find the critical value z/2, or (c) state that neither the normal distribution nor the t distribution applies. 30- The confidence level 99%, a is not known, and the histogram of 54 player salaries (in thousands of dollars) of football players on a team is as shown. 20- 10- 0- O 4000 8000 12000 1600 20000 Salary (thousands of dollars) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A t4/2= (Round to two decimal places as needed.) Za12= (Round to two decimal places as needed.) OB. OC. Neither the normal distribution nor the t distribution applies.
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Assume that we want to construct a confidence interval. Do one of the following, as appropriate: (a) find the critical value to/2. (b) find the critical value Zα/2, or (c) state that neither the normal distribution nor the t distribution applies. Here are summary statistics for randomly selected weights of newborn girls: n=218, x = 30.4 hg, s = 7.6 hg. The confidence level is 99%. ... Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. ta/2= (Round to two decimal places as needed.) OB. Za/2 (Round to two decimal places as needed.) OC. Neither the normal distribution nor the t distribution applies.
Assume that we want to construct a confidence interval. Do one of the following, as appropriate: (a) find the critical value ty /2, (b) find the critical value z,/2, or (c) state that neither the normal distribution nor the t distribution applies. 40- 30- The confidence level is 95%, o = 3827 thousand dollars, and the histogram of 61 player salaries (in thousands of dollars) of football players on a team is as shown. 20- 10- 4000 8000 12000 16000 20000 Salary (thousands of dollars) ..... Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. ta/2= %3D (Round to two decimal places as needed.) ОВ. Za/2 = (Round to two decimal places as needed.) O C. Neither the normal distribution nor the t distribution applies. Frequency

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