1 answer

It is recommended that the daily intake of sodium be 2600 mg per day. From a previous study on a

Question:

It is recommended that the daily intake of sodium be 2600 mg per day. From a previous study on a particular ethnic group, the prior distribution of sodium intake is believed to be normal with mean 3000 mg and standard deviation 300 mg. If a recent survey resulted in a mean of 3500 mg and standard deviation of 350 mg. Obtain a 99% Credible Interval for the mean intake of sodium for this ethnic group. Let n=1

.

You don't have to solve this because I know how to solve for a simple confidence interval. My question is, which distribution do we use for this when the sample size is 1? My first instinct is to use t, but what would be the degrees of freedom?


Answers

Answer to the question)
This is the scenario of one sample mean confidence interval

It can either be Z confidence interval or T confidence interval

.

Now when the population standard deviation (σ) value is provided, we always use the Z confidence interval formula

If the value of population standard deviation ( σ) is not provided, only then we switch to the T confidence interval formula

.

The formulae for both the interval are exactly same, just the t critical value is replaced by Z critical value

in case of Z critical value you need to depend on the degree of freedom value

.

Solution:

Formula of Z confidence interval is:

(x bar - z * σ/ sqrt( n) ) . ( x bar + z * σ/ sqrt( n) )

where:

x bar = sample mean = 3500 mg

σ = 300 mg [ population standard deviation is provided in the question]

n = sample size = 1

Value of Z critical value for 99% confidence level is:

(b) Confidence Interval Critical Values z Critical Value z 1.04 1.15 1.28 1.44 1.645 1.96 2.33 2.58 Level of Confidence c 0.7

.

Thus we get Z 2.58

.

On plugging these values we get:

(3500 -2.58 * 300/sqrt( 1) , 3500 +2.58 *300/sqrt(1) )

(2726 , 4274)

.

Similar Solved Questions

1 answer
Determine the maturity date and compute interest for each note. (Use 360 days a year. Do...
Determine the maturity date and compute interest for each note. (Use 360 days a year. Do not round intermediate calculations.) Period of Note Contract Interest Principal $25,000 (Term) 60 days 90 days 45 days Note Date Rate March 16 6% 1. May 08 October 28 2. 30,000 18,000 8 3. 4 Interest Maturity M...
1 answer
Elwood had to retire early because of a job-related injury. During the current year, he receives...
Elwood had to retire early because of a job-related injury. During the current year, he receives $10,000 in Social Security benefits. In addition, he receives $6,000 in cash dividends on stocks that he owned and $8,000 in interest on tax-exempt bonds. Assuming that Elwood is single, what is his gros...
2 answers
Means-testing in income redistribution programs can create perverse incentives. This means that the structure of the...
Means-testing in income redistribution programs can create perverse incentives. This means that the structure of the program: A. makes income distribution worse rather than better. B. reduces income mobility, particularly between generations. C. induces people to do things that are inefficient. D. i...
1 answer
07. Name one reason why it is difficult to produce antibacterial agents to treat tuberculosis. 08....
07. Name one reason why it is difficult to produce antibacterial agents to treat tuberculosis. 08. Besides mutation and change in protein structure, name other methods that may lead to developing resistance available to microorganisms....
1 answer
On December 31, 2015, Dab Industries reported a prepaid insurance expense account balance of $2,500 and...
On December 31, 2015, Dab Industries reported a prepaid insurance expense account balance of $2,500 and during 2016 the overall account balance (i.e. reported by the company on its financial statements) decreased by $1,300. During 2016, cash payments for future insurance coverage totaled $5,000. Sel...
1 answer
(15 points) George sells pepperoni pizzas at $25 per pizza from a stall on the beach.  ...
(15 points) George sells pepperoni pizzas at $25 per pizza from a stall on the beach.   George’s pays $30 per hour to rent his stall and pays his worker $10 per hour to make and sell the pizzas. The ingredients cost $15 per pizza. These are George’s only costs. NOTE: The hour...
1 answer
O The National Football League (NFL) polls fans to develop a rating for each football game....
O The National Football League (NFL) polls fans to develop a rating for each football game. Each game is rated on a scale from 0 (forgettable) to 100 (memorable). The fan ratings for a random sample of 12 games follow 57 61 86 75 72 73 19 57 79 79 82 75 a. Develop a point estimate of mean fan rating...
1 answer
Question 23 (1 point) During the latest year. XYZ Corporation has total sales of $400,000. net...
Question 23 (1 point) During the latest year. XYZ Corporation has total sales of $400,000. net income of 10000, and its year end total sses were S 500 000. The firm's total debt to total assets ratio was 30%, what is firm's profit margin? (Enter your answers as a decimal rounded to 4 decimal...
1 answer
Question 3 (1 point) Universal Travel Inc. borrowed $500,000 on November 1, 2021, and signed a...
Question 3 (1 point) Universal Travel Inc. borrowed $500,000 on November 1, 2021, and signed a 12- month note bearing interest at 6%. Interest is payable in full at maturity on October 31, 2022. In connection with this note, Universal Travel Inc. should report interest payable at December 31, 2021, ...
1 answer
Do you think that Wollstonecraft believes in her own arguments about why God wants men and...
Do you think that Wollstonecraft believes in her own arguments about why God wants men and women to be equal?...
1 answer
Consider an economy in which taxes, planned investment, government spending on goods and services, and net...
Consider an economy in which taxes, planned investment, government spending on goods and services, and net exports are autonomous, but consumption and planned investment change as the interest rate changes. You are given the following information concerning autonomous consumption, the marginal prope...
1 answer
How do you find a polynomial function of degree 4 with -2 as a zero of multiplicity 3 and 0 as a zero of multiplicity 1?
How do you find a polynomial function of degree 4 with -2 as a zero of multiplicity 3 and 0 as a zero of multiplicity 1?...
1 answer
1. Which one of the following is the most accurate description of a monopolist? a sole...
1. Which one of the following is the most accurate description of a monopolist? a sole producer of a narrowly defined product class, such as brown, Grade A eggs produced in Eagle County, Colorado A) B) a firm that is very large relative to all its competitors within a narrow product class C) a sole ...
1 answer
QUESTION 11 In Jefferson county, the mean water usage per household for the month of January...
QUESTION 11 In Jefferson county, the mean water usage per household for the month of January 2018 was .060 acre-feet (an acre-foot is the amount of water necessary to cover one acre to a depth of one foot.) This figure is based on the usage of all households in the county during that month. In Janua...
1 answer
Martex, a new company, completed these transactions. What will Martex's total assets equal? 1. Stockholders invested...
Martex, a new company, completed these transactions. What will Martex's total assets equal? 1. Stockholders invested $58,000 cash and inventory with a fair value of $29,000. 2. Sales on account, $20,000 OA. ⓔB. O C. OD. $107,000 $87,000 $58,000 $78,000...
1 answer
Cullumber Monograms sells stadium blankets that have been monogrammed with high school and university emblems. The...
Cullumber Monograms sells stadium blankets that have been monogrammed with high school and university emblems. The blankets retail for $42 throughout the country to loyal alumni of over 3,300 schools. Cullumber’s variable costs are 42% of sales; fixed costs are $116,000 per month. Cullumber cu...