# Question: A variable of two populations has a mean of 7 9

A variable of two populations has a mean of 7.9 and a standard deviation of 5.4 for one of the populations and a mean of 7.1 and a standard deviation of 4.6 for the other population.

Moreover, the variable is normally distributed on each of the two populations.

a. For independent samples of sizes 3 and 6, respectively, determine the mean and standard deviation of x1 − x2.

b. Can you conclude that the variable x1 − x2 is normally distributed? Explain your answer.

c. Determine the percentage of all pairs of independent samples of sizes 4 and 16, respectively, from the two populations with the property that the difference x1 − x2 between the sample means is between − 3 and 4.

Moreover, the variable is normally distributed on each of the two populations.

a. For independent samples of sizes 3 and 6, respectively, determine the mean and standard deviation of x1 − x2.

b. Can you conclude that the variable x1 − x2 is normally distributed? Explain your answer.

c. Determine the percentage of all pairs of independent samples of sizes 4 and 16, respectively, from the two populations with the property that the difference x1 − x2 between the sample means is between − 3 and 4.

**View Solution:**## Answer to relevant Questions

To obtain the sampling distribution of the difference between two sample means for independent samples, as stated in Key Fact 10.1 on page 394, we need to know that, for independent observations, the difference of two ...x1 = 115.1, s1 = 79.4, n1 = 51, x2 = 24.3, s2 = 10.5, n2 = 19 We have provided summary statistics for independent simple random samples from two populations. Preliminary data analyses indicate that the variable under ...The Federal Bureau of Prisons publishes data in Prison Statistics on the times served by prisoners released from federal institutions for the first time. Independent random samples of released prisoners in the fraud and ...Refer to Exercise 10.40 and obtain a 98% confidence interval for the difference between the mean absolute pointing errors for males and females. In this section, we introduced the pooled t-test, which provides a method for comparing two population means. In deriving the pooled t-test, we stated that the variable cannot be used as a basis for the required test ...Post your question