Question

In: Statistics and Probability

We draw a random sample of size 36 from a population with standard deviation 3.2. If...

We draw a random sample of size 36 from a population with standard deviation 3.2. If the sample mean is 27, what is a 95% confidence interval for the population mean?

Solutions

Expert Solution

Solution :


Given that,

Point estimate = sample mean =     = 27

Population standard deviation =    = 3.2

Sample size n =36

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96   ( Using z table )

Margin of error = E =   Z/2    * ( /n)
= 1.96 * ( 3.2 / 36 )

= 1.045
At 95% confidence interval estimate of the population mean
is,

- E < < + E

27 - 1.045 <   < 27 + 1.045

(25.955 , 28.045)


Related Solutions

We draw a random sample of size 36 from a population with standard deviation 3.2. If...
We draw a random sample of size 36 from a population with standard deviation 3.2. If the sample mean is 27, what is a 95% confidence interval for the population mean? [26.7550, 28.2450] [25.9547, 28.0453] [25.8567, 28.1433] [26.8401, 27.1599]
4 We draw a random sample of size 40 from a population with standard deviation 2.5....
4 We draw a random sample of size 40 from a population with standard deviation 2.5. Show work in excel with formulas a If the sample mean is 27, what is a 95% confidence interval for the population mean? b If the sample mean is 27, what is a 99% confidence interval for the population mean? c If the sample mean is 27, what is a 90% confidence interval for the population mean? d If the sample mean is 27...
A simple random sample of size n=36 is obtained from a population with mean=89 and standard...
A simple random sample of size n=36 is obtained from a population with mean=89 and standard deviation = 6 ​(c) What is P ( x overbar less than or equal to 86.65)​? ​ (d) What is P(88.5 < x overbar < 91.25)? ​(a) Describe the sampling distribution of x overbar. ​(b) What is P ( x overbar > 90.85 )?
A random sample of size 16 from a normal distribution with known population standard deviation �...
A random sample of size 16 from a normal distribution with known population standard deviation � = 3.1 yields sample average � = 23.2. What probability distribution should we use for our sampling distributions of the means? a) Normal Distribution b) T-distribution c) Binomial Distribution d) Poisson Distribution What is the error bound (error) for this sample average for a 90% confidence interval? What is the 90% confidence interval for the population mean?
We draw a random sample of size 49 from a normal population with variance 2.1. If...
We draw a random sample of size 49 from a normal population with variance 2.1. If the sample mean is 21.5, what is a 99% confidence interval for the population mean?
For a random sample of size 64 from a population with mu=24 and standard deviation sigma=1.5....
For a random sample of size 64 from a population with mu=24 and standard deviation sigma=1.5. State the center, variation, and shape of the sampling distribution for samples of size 64. Justify your answer. Find the probability that the sample mean exceeds 24.3. Draw a fully labeled picture that illustrates the probability, and write down your answer using probability notation.
5. A random sample of size n = 36 is obtain from a population with µ=...
5. A random sample of size n = 36 is obtain from a population with µ= 60 and standard deviation 12 (a). Describe the sampling distribution . (b). What is P(76.5 << 85.5 )?
A random sample of size n = 36 is obtain from a population with µ= 80,...
A random sample of size n = 36 is obtain from a population with µ= 80, and standard deviation =18. (a). Describe the sampling distribution . (b). What is P(77 << 85 )?
9. If a sample of size 64 is drawn from a population with a standard deviation...
9. If a sample of size 64 is drawn from a population with a standard deviation of 80, the standard deviation of sample means would equal _______. A. 10.000 B. 1.250 C. 0.125 D. 0.800
From a random sample from normal population, we observed sample mean=84.5 and sample standard deviation=11.2, n...
From a random sample from normal population, we observed sample mean=84.5 and sample standard deviation=11.2, n = 16, H0: μ = 80, Ha: μ < 80.  State your conclusion about H0 at significance level 0.01. choices: A. Test statistic: t = 1.61. P-value = 0.9356. Reject the null hypothesis. There is sufficient evidence to conclude that the mean is less than 80. The evidence against the null hypothesis is very strong. B. Test statistic: t = 1.61. P-value = 0.0644. Do...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT