Basic Computation: Testing M1 2 M2 A random sample of 49 measurements from a population with population standard deviation 3 had a sample mean of 10. An independent random sample of 64 measurements from a second population with population standard deviation 4 had a sample mean of 12. 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

The sample statistics follows a standard normal distribution since the sample size are large enough.

Step-by-step explanation:

Given that:

First population:

Sample size = 49

Population standard deviation  = 3

Sample mean = 10

Second population:

Sample size = 64

Population standard deviation = 4

Sample mean = 12

The sample statistics follows a standard normal distribution since the sample size are large enough.

The null and alternative hypotheses can be computed as:

Level of significance  = 0.01

Using the  Z-test statistics;

Z = - 3.037

Z - 3.04

The P-value = 2P (z < -3.04)

From the z tables

= 2 × (0.00118)

= 0.00236

Thus, since P-value is less than the level of significance, we fail to reject the null hypotheses

a4 - 3a2 - 1

step-by-step explanation:

step   1   :

equation at the end of step   1   :

  ((a4) -   3a2) -   1

step   2   :

trying to factor by splitting the middle term

2.1     factoring   a4-3a2-1  

the first term is,   a4   its coefficient is   1 .

the middle term is,   -3a2   its coefficient is   -3 .

the last term, "the constant", is   -1