Question

User Before the election, a poll of 60 voters found the proportion who support the Green candidate to be 25%. Calculate the 90% confidence interval for the population parameter. (Give your answers as a PERCENTAGE rounded to TWO DECIMAL PLACES: exclude any trailing zeros and DO NOT INSERT THE % SIGN) Give the lower limit of the 90% confidence interval Give the upper limit of the 90% confidence interval

169

likes
844 views

Answer to a math question User Before the election, a poll of 60 voters found the proportion who support the Green candidate to be 25%. Calculate the 90% confidence interval for the population parameter. (Give your answers as a PERCENTAGE rounded to TWO DECIMAL PLACES: exclude any trailing zeros and DO NOT INSERT THE % SIGN) Give the lower limit of the 90% confidence interval Give the upper limit of the 90% confidence interval

Expert avatar
Maude
4.7
97 Answers
To calculate the 90% confidence interval for the population parameter, we can use the formula:

\text{Confidence Interval} = \text{Sample Proportion} \pm \text{Critical Value} \times \text{Standard Error}

where:
- Sample Proportion is the proportion of voter support found in the poll (p̂)
- Critical Value is the value from the standard normal distribution corresponding to the desired confidence level (Z)
- Standard Error is the standard deviation of the sample proportion (σp̂)

Step 1: Calculate the Sample Proportion (p̂)
Given that the proportion of voters supporting the Green candidate is 25%, we can say that p̂ = 0.25.

Step 2: Calculate the Critical Value (Z)
Since we want a 90% confidence interval, we need to find the critical value that corresponds to a 5% margin of error on each side of the mean. Using a standard normal distribution table or calculator, we find that the critical value Z for a 90% confidence level is approximately 1.645.

Step 3: Calculate the Standard Error (σp̂)
The standard error of the sample proportion can be calculated using the formula:
\sigma_{p̂} = \sqrt{\frac{p̂(1-p̂)}{n}}

where n is the sample size. In this case, the sample size is 60.

\sigma_{p̂} = \sqrt{\frac{0.25(1-0.25)}{60}}
\sigma_{p̂} = \sqrt{\frac{0.1875}{60}}
\sigma_{p̂}\approx0.0559

Step 4: Calculate the Confidence Interval
Now we can plug in the values into the confidence interval formula:

\text{Confidence Interval}=0.25\pm1.645\times0.0559

Step 5: Calculate the Lower Limit
\text{Lower Limit}=0.25-1.645\times0.0559=0.25-0.0919555=0.1580445\approx15.80\%

Step 6: Calculate the Upper Limit
\text{Upper Limit}=0.25+1.645\times0.0559=0.25+0.0919555=0.3419555\approx34.20\%

Answer:
The lower limit of the 90% confidence interval is approximately 15.80%
The upper limit of the 90% confidence interval is approximately 34.20%

Frequently asked questions (FAQs)
What is the value of (4 + 6) x (3 - 2) / 5?
+
Question: How many obtuse triangles can be formed using the side lengths of 4, 5, 6, 8, and 10 units?
+
What is the area of a square if the length of its side is 5 units?
+
New questions in Mathematics
A sample is chosen from a population with y = 46, and a treatment is then administered to the sample. After treatment, the sample mean is M = 47 with a sample variance of s2 = 16. Based on this information, what is the value of Cohen's d?
The strength of Kefexin oral suspension is 100 mg/ml. Nora has been prescribed cefalexin at a dose of 50 mg/kg/day divided in two single doses. Nora weighs 14 kg. How many milliliters of solution for Nora should be given as a single dose?
What is the coefficient of elasticity of the material that must be placed on the heel of the 10 cm high clog, with a base area of 2 cm² so that it deforms only 2 cm when the force on it will be a maximum of 600 N.
Karina has a plot of 5,000 square meters in which she has decided that 60% of it will be used to plant vegetables. Of this part, 12% will be dedicated to planting lettuce. How much surface area of the plot will be used for cultivation?
5) A family with a father, mother and 3 children must sit on five chairs in a row and the only restriction is that the mother must be at one end. In how many different ways can they be seated?
Evaluate limx→∞tan−1(x) using that y=tan−1(x) exactly when x=tan(y) . (Hint: Both tan and tan−1 are continuous!)
math question a bookstore announces a promotion valid for the same purchase as follows: buy a book and get 10% off the total purchase! buy two books and get 20% off your total purchase! buy three or more books and get 30% off your total purchase! Marcelo wanted to buy three books that cost 20.00 each without discount but he decided to buy two books in one day and another purchase with the third book the next day. If he had bought the three books at once he would have saved the following amount.
a bank finds that the balances in its savings accounts are normally distributed with a mean of $500 and a standard deviation off of $40. What is the probability that a randomly selected account has a balance of more than $400?
Let f(x) = x² − 1. Find the equation of the tangent line to the graph of f at the point x0 = 2.
solve for x 50x+ 120 (176-x)= 17340
Log5 625
determine the polynomial F of degree 2 that interpolates. f at points (0;1) (2;5) (4;6). calculate F(0.8). Note: Using the polynomial expression with difference operator.
What’s the slope of a tangent line at x=1 for f(x)=x2. We can find the slopes of a sequence of secant lines that get closer and closer to the tangent line. What we are working towards is the process of finding a “limit” which is a foundational topic of calculus.
The Humane Society has asked for our help again this week. Currently they are charging $50 for an adoption fee. Unfortunately they just pulled this number out of the air and do not know why they are charging this amount. They would like to charge an amount that covers all the adoption costs – both the variable costs for adoptions as well as the fixed cost for the kennel portion of the Humane Shelter operations. We can help them by doing a breakeven analysis. During a client meeting we gathered these facts. There are 2 part-time employees that each earn $1000 per month. The utilities for the kennel area (water, electricity) are $200 per month. The average food cost for animals in the kennel is $800 per month. In addition, each animal that is adopted receives a rabies vaccination that costs $4 and is micro-chipped that costs $6. At the current cost of $50, how many animals must be adopted to break-even? What would break-even be at a $60 adoption fee? What would break-even be if the fee were lowered to $40? The newspaper has suggested that the Humane Society advertise to increase pet adoptions. The package that they have recommended costs $1000 for a very small ad run every day for a month. If the Humane Society does this extra advertising, how will it affect breakeven? Based on what you have learned about elasticity, what price do you recommend for the adoption fee?
If a two-branch parallel current divider network, if the resistance of one branch is doubled while keeping all other factors constant, what happens to the current flow through that branch and the other branch? Select one: a. The current through the doubled resistance branch remains unchanged, and the current through the other branch decreases. b. The current through the doubled resistance branch decreases, and the current through the other branch remains unchanged. c. The current through the doubled resistance branch increases, and the current through the other branch remains unchanged. d. The current through both branches remain unchanged.
A loan is repaid with payments of $2226 made at the end of each month for 12 years. If interest on the loan is 5.2%, compounded semi-annually, what is the initial value of the loan? Enter to the nearest cent (two decimals). Do not use $ signs or commas.
A person runs 175 yards per minute write a variable that represents the relationship between time and distance
How much does 7.2 moles of ammonium dichromate weigh? (NH4)2Cr2O7
Carmen's age was twice as old as Luis was when Carmen was Luis's age. When Luis is Carmen's age, their ages will add up to 112.
the length of the fenced in area is to be 5 ft greater than the width and the total amount of fencing to be used is 89 ft find the width and length