### Constructing a Confidence Interval#### Problem StatementAssume that we want to construct a confidence interval. Do one of the following, as appropriate: - (a) find the critical value \( t_{\alpha/2} \)- (b) find the critical value \( z_{\alpha/2} \)- (c) state that neither the normal distribution nor the t distribution applies.#### Provided DataHere are summary statistics for randomly selected weights of newborn girls:- Sample size (\( n \)): 190- Sample mean (\( \bar{x} \)): 29.7 hg- Sample standard deviation (\( s \)): 6.6 hgThe confidence level is 95%.#### InstructionsSelect the correct choice below and, if necessary, fill in the answer box to complete your choice.#### Options- **A.** \( t_{\alpha/2} = \) [ ] (Round to two decimal places as needed.)- **B.** \( z_{\alpha/2} = \) [ ] (Round to two decimal places as needed.)- **C.** Neither the normal distribution nor the t distribution applies.---### Detailed Explanation of the Options- **Option A: Using the t-distribution** - The t-distribution is typically used when the sample size is small (\( n < 30 \)) and/or the population standard deviation is unknown. - You need to find the critical value \( t_{\alpha/2} \) for the given confidence level and degrees of freedom (\( df = n - 1 \)).- **Option B: Using the z-distribution** - The z-distribution is used when the sample size is large (\( n \geq 30 \)) and the population standard deviation is known or can be approximated well by the sample standard deviation. - You need to find the critical value \( z_{\alpha/2} \) for the given confidence level.- **Option C: Neither distribution applies** - This would be applicable in cases where the underlying assumptions for both the normal distribution (z-distribution) and t-distribution are violated or not met.This kind of decision-making process is fundamental when performing inferential statistics to ensure that the resulting confidence intervals are valid based on the specified criteria and known data properties.

Name: ### Constructing a Confidence Interval#### Problem StatementAssume th
Uploaded: 2024-03-20T07:07:12.000Z
Channel: Bartleby
Description: ### Constructing a Confidence Interval#### Problem StatementAssume that we want to construct a confidence interval. Do one of the following, as appropriate: - (a) find the critical value \( t_{\alpha/2} \)- (b) find the critical value \( z_{\alpha/2

Given information- Sample size, n = 190 Sample mean, x-bar = 29.7 hg Sample standard deviation, s =…

Math

Statistics

Assume that wve want to construct a confidence interval. Do one of the following, as appropriate: (a) find the critical value ta/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= 190, x 29 7 hg, s = 6.6 hg. The confidence level is 95%.

Assume that wve want to construct a confidence interval. Do one of the following, as appropriate: (a) find the critical value ta/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= 190, x 29 7 hg, s = 6.6 hg. The confidence level is 95%.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Similar questions

One year, the mean age of an inmate on death row was 40.9 years. A sociologist wondered whether the mean age of a death-row inmate has changed since then. She randomly selects 32 death-row inmates and finds that their mean age is 39.4, with a standard deviation of 9.5. Construct a 95% confidence interval about the mean age. What does the interval imply? Click the icon to view the table of critical t-values. Choose the correct hypotheses. Ho: H₁: (Type integers or decimals. Do not round.) Construct a 95% confidence interval about the mean age. With 95% confidence, the mean age of a death row inmate is between What does the interval imply? years and years. (Round to two decimal places as needed.) O A. Since the mean age from the earlier year is contained in the interval, there is sufficient evidence to conclude that the mean age had changed. B. Since the mean age from the earlier year is not contained in the interval, there is not sufficient evidence to conclude that the mean age had…
Blood sugars from eight patients in a rural clinic were recorded last summer by the local physician. The blood sugars results were: 120, 145, 200, 250, 79, 100, 894, 255 mg/d1. The standard deviation was 5. Calculate the 95% Confidence Interval (CI) of the mean blood sugars.
Lorraine computed a confidence interval for μ based on a sample of size 41. Since she did not know σ, she used s in her calculations. Lorraine used the normal distribution for the confidence interval. Are Lorraine's methods correct? Explain.
d) For the following data (80, 40, 62, 70, 30, 82), the standard deviation is 24 O 24.5 O 25 O 25.5 O none of all above O
Mrs. Gallas wanted to estimate the average weight of an Oreo cookie to determine if theaverage weight was less than advertised. She selected a random sample of 30 cookies andfound the weight of each cookie (in grams). The mean weight was = 11.1921 grams with astandard deviation of sx = 0.0817 grams. Make a 95% confidence interval to estimate the truemean weight of an Oreo. 1. What is the formula for calculating the standard deviation of the sampling distribution of x? 2.What condition must be met to use this formula? Has it been met?
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 Zu/2, or (c) state that neither the normal distribution nor the t distribution applies. The confidence level is 95%, o is not known, and the histogram of 64 player salaries (in thousands of dollars) of football players on a team is as shown. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. /2² (Round to two decimal places as needed.) OB. Z/2 = (Round to two decimal places as needed.) O C. Neither the normal distribution nor the t distribution applies. ← Frequency 40- 30- 20- 10- ó 4000 8000 12000 16000 20000 Salary (thousands of dollars) G
A researcher is interested in studying the use of hypnosis to relieve pain. She took a random sample of 16 subjects and measured their sensory ratings. The mean of the sensory ratings was found to be 7.5 and standard deviation to be 2.3. It is known that the sensory ratings are normally distributed. Construct a 99% confidence interval for the mean sensory ratings of the population. a) (5.81, 9.19) b) (6.27, 8.73) c) (6.36, 8.64) d) (6.02, 8.98)
The Pizza Shop wanted to determine what proportion of its customers ordered only cheese pizza. Out of 80 customers surveyed, 15 ordered cheese pizza. They want a 99% confidence interval of the true proportion of customers who order only cheese pizza. Which type of confidence interval should we use here? a confidence interval for the mean using a table value from the standard normal distribution. a confidence interval for the mean using a table value from the t distribution. a confidence interval for a proportion using a table value from the standard normal distribution. a confidence interval for proportion using a table value from the t distribution.
The ages of registered voters in Smith County are normally distributed with a population standard deviation of 3 years and an unknown population mean. A random sample of 18 voters is taken and results in a sample mean of 55 years. Find the margin of error for a 95% confidence interval for the population mean. z0.10z0.10 z0.05z0.05 z0.025z0.025 z0.01z0.01 z0.005z0.005 1.282 1.645 1.960 2.326 2.576 You may use a calculator or the common z values above. Round the final answer to two decimal places.
Jose wants to advertise how many chocolate chips are in each Big Chip cookie at his bakery. He randomly selects a sample of 52 cookies and finds that the number of chocolate chips per cookie in the sample has a mean of 19.5. The population standard deviation is 2.5. What is the 90% confidence interval for the number of chocolate chips per cookie for Big Chip cookies? Assume the data is from a normally distributed population.Round answers to 3 decimal places where possible.
A nutritionist selected a random sample of n = 50 adult males. The average daily intake of dairy products was found to be x (bar above) = 756 grams per day, with a standard deviation of s = 35 grams per day. Use this sample information to construct a 95% confidence interval for the mean daily intake of dairy products for men.
Isabella wants to advertise how many chocolate chips are in each Big Chip cookie at her bakery. She randomly selects a sample of 62 cookies and finds that the number of chocolate chips per cookie in the sample has a mean of 7.8 and a standard deviation of 1.3. What is the 90% confidence interval for the number of chocolate chips per cookie for Big Chip cookies? Assume the data is from a normally distributed population. Round answers to 3 decimal places where possible.