Assuming that a sampling distribution is symmetric and bell-shaped, use the sample statistic and standard error below to give a 95% confidence interval for the parameter being estimated. 𝑝̂ = 0.4, standard error = 0.09What population parameter is being estimated in this case?
Question
Assuming that a sampling distribution is symmetric and bell-shaped, use the sample statistic and standard error below to give a 95% confidence interval for the parameter being estimated. 𝑝̂ = 0.4, standard error = 0.09What population parameter is being estimated in this case?
Solution
The population parameter being estimated in this case is the population proportion (p).
Now, let's calculate the 95% confidence interval for the parameter.
A 95% confidence interval is typically associated with approximately 1.96 standard errors in a normal distribution (which is a good approximation of a symmetric, bell-shaped sampling distribution).
The formula for a confidence interval is:
Confidence Interval = sample statistic ± (critical value * standard error)
Given that the sample statistic (𝑝̂) is 0.4 and the standard error is 0.09, we can substitute these values into the formula:
Confidence Interval = 0.4 ± (1.96 * 0.09)
This simplifies to:
Confidence Interval = 0.4 ± 0.1764
So, the 95% confidence interval for the population proportion (p) is (0.2236, 0.5764).
This means we are 95% confident that the true population proportion lies between 0.2236 and 0.5764.
Similar Questions
You want to compute a 90% confidence interval for the mean of a population with unknown standard deviation. The sample size is 30. The correct distribution value for calculating the required confidence interval is:-Group of answer choices1.961.64491.6991.6971.311
Use the bootstrap distribution for a sample proportion above to estimate a 95% confidence interval. Give your answers to 2 decimal places (2dp).Lower Limit: Answer 1 Question 16 Upper Limit: Answer 2 Question 16Give the symbol for the parameter being estimated in this case: Answer 3 Question 16
A sample of 230 observations is selected from a normal population with a population standard deviation of 26. The sample mean is 18. (Use t Distribution Table & z Distribution Table.)Required:a. Determine the standard error of the mean. (Round your answer to 3 decimal places.)c. Determine the 99% confidence interval for the population mean. (Round your answers to 3 decimal places.)
Let’s say you wish to construct a sampling distribution of sample size 100 for the proportion of people that voted for AAP. Suppose the population standard deviation is known to be 0.7, what is the interval in which the mean of the sampling distribution will belong at a 90% confidence level?(0.485, 0.675) (0.572, 0.588)(0.465, 0.695)(0.503, 0.657)
It is believed that 11% of all Americans are left-handed. In a random sample of 500 students from a particular college with 52407 students, 47 were left-handed. Find a 97% confidence interval for the percentage of all students at this particular college who are left-handed.P: Parameter What is the correct parameter symbol for this problem? What is the wording of the parameter in the context of this problem? A: AssumptionsSince information was collected from each object, what conditions do we need to check? Check all that apply. 𝑛≥30 or normal population.σσ is known.𝑛(1-𝑝)≥10𝑛(𝑝̂)≥10σσ is unknown.𝑁≥20𝑛𝑛(1-𝑝̂)≥10𝑛𝑝≥10 Check those assumptions: 1. 𝑛𝑝^= which is 2. 𝑛(1-𝑝^)= which is 3. 𝑁= which is If no N is given in the problem, use 1000000N: Name the procedure The conditions are met to use a .I: Interval and point estimate The symbol and value of the point estimate on this problem are as follows: = Leave answer as a fraction. The interval estimate for is ( , ) Round endpoints to 3 decimal places.C: Conclusion We are % confident that the is between % and %
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.