Question

In: Math

independent random sample of size n1=16 and n2= 25 from a normal population with standard deviation1=4.8...

independent random sample of size n1=16 and n2= 25 from a normal population with standard deviation1=4.8 and standard deviation 2=3.5 have the mean x bar1=18.2 and xbar2=23.4 find the 90% confidence interval for mew1-mew 2

Solutions

Expert Solution

Given,

1 = 18.2, 2 = 23.4 , S1 = 4.8 , S2 = 3.5, n1 = 16, n2 = 25

Pooled standard deviation Sp= Sqrt ( [ (n1-1) S21 + (n2 - 1)S22 ] / n1 + n2 - 2 )

= Sqrt( 15 * 4.82 + 24 * 3.52 / (16 + 25 - 2) )

= 4.0497

df = n1 + n2 - 2 = 16 + 25 - 2 = 39

t critical value at 0.10 siginficance level for 39 df = 1.685

90% confidence interval for 1 - 2 is

(1 - 2) - t * Sp * sqrt(1/n1 + 1/n2) < 1 - 2 < (1 - 2) + t * Sp * sqrt(1/n1 + 1/n2)

(18.2-23.4) - 1.685*4.0497*sqrt(1/16+1/25) < 1-2 < (18.2 - 23.4) + 1.685*4.0497*sqrt(1/16+1/25)

-5.2 - 2.1847 < 1 - 2 < -5.2 + 2.1847

-7.3847 <  1 - 2 < -3.0153

Confidence interval for  1 - 2 is (-7.3847 , -3.0153 )


Related Solutions

A random sample of size n1 = 16 is selected from a normal population with a...
A random sample of size n1 = 16 is selected from a normal population with a mean of 74 and a standard deviation of 9. A second random sample of size n2 = 7 is taken from another normal population with mean 68 and standard deviation 11. Let X1and X2 be the two sample means. Find: (a) The probability that X1-X2 exceeds 4. (b) The probability that 4.8 ≤X1-X2≤ 5.6. Round your answers to two decimal places (e.g. 98.76).
A random sample of size n1 = 14 is selected from a normal population with a...
A random sample of size n1 = 14 is selected from a normal population with a mean of 74 and a standard deviation of 6. A second random sample of size n2 = 9 is taken from another normal population with mean 70 and standard deviation 14. Let X¯1and X¯2 be the two sample means. Find: (a) The probability that X¯1-X¯2 exceeds 3. (b) The probability that 4.4 ≤X¯1-X¯2≤ 5.4.
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?
3. Independent random samples of n1 = 16 and n2 = 13 observations were selected from...
3. Independent random samples of n1 = 16 and n2 = 13 observations were selected from two normal populations with equal variances. The sample means and variances are shown below: Population 1 Population 2 Sample size 16 13 Sample mean 34.6 32.2 Sample variance 4.0 4.84 a) Suppose you wish to test if there is difference between the population means with significance level of α = 0.05. State the null and alternative hypotheses that you use for the test. b)...
An independent random sample is selected from an approximately normal population with an unknown standard deviation....
An independent random sample is selected from an approximately normal population with an unknown standard deviation. Find the p-value for the given set of hypotheses and T test statistic. Also determine if the null hypothesis would be rejected at alpha = 0.05. a. HA : mu > 0, n = 11, t = 1.91 b. HA: mu < 0, n = 17, t = -3.45
Random sample of size n=19 is taken from a Normal population, sample mean is 11.5895, standard...
Random sample of size n=19 is taken from a Normal population, sample mean is 11.5895, standard deviation is 1.0883. 1. At the 2% level, test whether it is reasonable to believe that the true population variance is larger than 1. Using the scenario from above, do the following 2. Derive the power function. Show your work. 3. Using R, graph the power function for 0.5 < sigma^2 < 3.5. 4. Pretend that the sample size was actually 56. Plot this...
A random sample of n1 = 49 measurements from a population with population standard deviation σ1...
A random sample of n1 = 49 measurements from a population with population standard deviation σ1 = 5 had a sample mean of x1 = 8. An independent random sample of n2 = 64 measurements from a second population with population standard deviation σ2 = 6 had a sample mean of x2 = 11. Test the claim that the population means are different. Use level of significance 0.01. (a) Check Requirements: What distribution does the sample test statistic follow? Explain....
A random sample of size 15 is taken from a population assumed to be normal, with...
A random sample of size 15 is taken from a population assumed to be normal, with sample mean = 1.2 and sample variance = 0.6. Calculate a 95 percent confidence interval for population mean.
A sample of size 25 will be drawn from a population with mean 34 and standard...
A sample of size 25 will be drawn from a population with mean 34 and standard deviation 8. Find the probability that x− will be greater than 36.
a. A random sample of 25 is taken from a normal distribution with population mean =...
a. A random sample of 25 is taken from a normal distribution with population mean = 62, and population standard deviation = 7. What is the margin of error for a 90% confidence interval? b. Repeat the last problem if the standard deviation is unknown, given that the sample standard deviation is S=5.4
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT