n order to test the null hypothesis of equal means (alternative hypothesis says they are unequal), two simple random samples are obtained. In sample 1, the mean and standard deviation are 10 and 6 respectively. In sample 2, the mean and standard deviation are 16 and 4 respectively. Each sample is of size 6.The data are normally distributed. The true standard deviations of the two populations may be assumed to be equal. What can you say about the P-value for the test of equal means? --> It must be

Complete Question

In order to test the null hypothesis of equal means (alternative hypothesis says they are unequal), two simple random samples are obtained.In sample 1, the mean and standard deviation are 10 and 6 respectively.In sample 2, the mean and standard deviation are 16 and 4 respectively.Each sample is of size 6.The data are normally distributed.The true standard deviations of the two populations may be assumed to be equal.What can you say about the P-value for the test of equal means? -->

It must be that the resulting P-value must be

A) Greater than 0.2

B) Between 0.19 and 0.10

C) Between 0.09 and .05

D) Between .049 and .02

E) Less than 0.02

The correct option is B

Step-by-step explanation:

From the question we are told that

   The mean of sample 1 is  

   The standard deviation is  

   The mean of sample two is  

   The standard deviation is  

   The sample size for both samples is  

  The null hypothesis is  

  The alternative hypothesis is  

Generally the test statistics is mathematically represented as

=>      

=>      

From the z table  the area under the normal curve to the left corresponding to  -1.3646   is

Generally the p-value is mathematically represented as

=>  

=>  

So the p-value is  Between 0.19 and 0.10

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.