Question

In: Statistics and Probability

Use the given data to find the 95% confidence interval estimate of the population mean μ...

Use the given data to find the 95% confidence interval estimate of the population mean μ . Assume that the population has a normal distribution.

IQ scores of professional athletes:

Sample size n=25

Mean=103

Standard deviation s=15

Answer: ____ <μ< _____

Expert Solution

Solution :

Given that,

= 103

s =15

n =25

Degrees of freedom = df = n - 1 =25 - 1 = 24

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2= 0.05 / 2 = 0.025

t /2,df = t0.025,24 = 2.064 ( using student t table)

Margin of error = E = t/2,df * (s / $\sqrt$ n)

= 2.064 * (15 / $\sqrt$ 25)

= 6.19

The 95% confidence interval estimate of the population mean is,

- E < < + E

103 - 6.19 < <103 + 6.19

96.81 < < 109.19

orchestra answered 2 years ago

Use the given data to find the 95% confidence interval estimate of the population mean μ....

Use the given data to find the 95% confidence interval estimate of the population mean μ. Assume that the population has a normal distribution. IQ scores of professional athletes: Sample size n=20 Mean x¯¯¯=104 Standard deviation s=14 <μ<

Assume that a sample is used to estimate a population mean μ. Find the 95% confidence...

Assume that a sample is used to estimate a population mean μ. Find the 95% confidence interval for a sample of size 1037 with a mean of 38.4 and a standard deviation of 19.2. Enter your answer as a tri-linear inequality accurate to 3 decimal places. _______< μ < _______

Determine the 95% confidence interval estimate for the population mean of a normal distribution given n=144,...

Determine the 95% confidence interval estimate for the population mean of a normal distribution given n=144, sigma=105, and x overbar=1,200. The 95% confidence interval for the population mean is from to . (Round to two decimal places as needed. Use ascending order.

A 95% confidence interval estimate for a population mean is determined to be between 94.25 and...

A 95% confidence interval estimate for a population mean is determined to be between 94.25 and 98.33 years. If the confidence interval is increased to 98%, the interval would become narrower remain the same become wider

Construct a 95?% confidence interval to estimate the population mean using the following data. What assumptions...

Construct a 95?% confidence interval to estimate the population mean using the following data. What assumptions need to be made to construct this? interval? x?=93 ?=15 n=17 With 95?% ?confidence, when n=17 the population mean is between the lower limit of __ and the upper limit of __

Construct a 95% confidence interval to estimate the population mean using the data below. x̅= 46...

Construct a 95% confidence interval to estimate the population mean using the data below. x̅= 46 σ=12 n= 41 With 95% confidence, when n=41 the population mean is between a lower limit of ___ and upper limit of ___

Construct a 95% confidence interval to estimate the population mean using the following data. What assumptions...

Construct a 95% confidence interval to estimate the population mean using the following data. What assumptions need to be made to construct this interval? x(over bar x)= 83 s=19 n=16 What assumptions need to be made to construct this interval? A. The population is skewed to one side. B. The sample size is less than 30. C. The population mean will be in the confidence interval. D. The population must be normally distributed. With 95% confidence, when n=16 the population...

a) In order to estimate the population mean, μ, to within 3 at 95% confidence, what...

a) In order to estimate the population mean, μ, to within 3 at 95% confidence, what is the minimum sample size required? (Assumeσ=6.7). b) If just the population standard deviation were to increase, then the minimum sample size required would: decrease /increase c) If just the confidence level were to decrease (i.e. go from 95% to 90% confidence), then the minimum sample size required would: decrease/increase d) If just the bound within which μ was to be estimated were...

A 90% confidence interval for a population mean, μ, is given as (21.73, 24.64). This confidence...

A 90% confidence interval for a population mean, μ, is given as (21.73, 24.64). This confidence interval is based on a simple random sample of 41 observations. Calculate the sample mean and standard deviation. Assume that all conditions necessary for inference are satisfied. Use the t- distribution in any calculations.

Suppose I estimate μ, the mean of a population. I obtain estimate 6.5 and 95% confidence...

Suppose I estimate μ, the mean of a population. I obtain estimate 6.5 and 95% confidence interval (4.5, 8.5). A) Can I reject H0 : μ = 8 using at two-sided test at the 1% significance level? a) Yes. b) No. c) Not enough information to decide. B) Can I reject H0 : μ = 8 using at two-sided test at the 10% significance level? a) Yes. b) No. c) Not enough information to decide. C) Can I reject H0...