Aproducer of fine chocolates believes that the sales of two varieties of truffles differ significantly during the holiday season. the first variety is milk chocolate while the second is milk chocolate filled with mint. it is reasonable to assume that truffle sales are normally distributed with unknown but equal population variances. two independent samples of 18 observations each are collected for the holiday period. a sample mean of 12 million milk chocolate truffles sold with a sample standard deviation of 2.5 million. a sample mean of 13 million truffles filled with mint sold with a sample standard deviation of 2.3 million. use milk chocolate as population 1 and mint chocolate as population 2. assuming the population variances are equal, which of the following is the value of the appropriate test statistic?

Step-by-step explanation:

When we have two independent samples from two normal distributions with equal variances we are assuming that  

And the statistic is given by this formula:

Where t follows a t distribution with degrees of freedom and the pooled variance is given by this formula:

This last one is an unbiased estimator of the common variance

The system of hypothesis on this case are:

Null hypothesis:

Alternative hypothesis:

Or equivalently:

Null hypothesis:

Alternative hypothesis:

Our notation on this case :

represent the sample size for group 1

represent the sample size for group 2

represent the sample mean for the group 1

represent the sample mean for the group 2

represent the sample standard deviation for group 1

represent the sample standard deviation for group 2

First we can begin finding the pooled variance:

And the deviation would be just the square root of the variance:

And now we can calculate the statistic:

Now we can calculate the degrees of freedom given by:

And now we can calculate the p value using the altenative hypothesis:

If we compare the p value obtained and using the significance level assumed we have so we can conclude that we have enough evidence to FAIL to reject the null hypothesis.  

hello :

by applying the distributive property :

6 × 4.3 = 6 × ( 4 + 0.3 )

            =   (6 ×   4) + (6 ×   0.3)

            = 24 + 1.8

6 × 4.3 = 25.8

starting with:    

5 + x - 12 = 2x - 7   

5 + x - 12 - x = 2x - 7 - x (subtract x from both sides)   

5 - 12 = x - 7 (combine and cancel x's from both sides)   

5 - 12 + 7 = x - 7 + 7 (add 7 to both sides)   

0 = x (add numbers together on both sides)       

so in order for the equation to be true, x must be 0.   

trying x = -0.5   

5 + x - 12 = 2x - 7 (original equation)   

5 + -0.5 - 12 = 2(-0.5) - 7 (plug in value of x)   

5 + -0.5 - 12 = -1 - 7 (did multiplication)   

-7.5 = -8 (did addition on both sides)       

since -7.5 is obviously not equal to -8, the value of -0.5 for x is wrong.   

trying x = 0   

5 + x - 12 = 2x - 7 (original equation)   

5 + 0 - 12 = 2(0) - 7 (plug in value of x)   

5 + 0 - 12 = 0 - 7 (did multiplication)   

-7 = -7 (did addition on both sides)       

since -7 equals -7, that demonstrates that the value of 0 for x is correct.   

trying x = 1   

5 + x - 12 = 2x - 7 (original equation)   

5 + 1 - 12 = 2(1) - 7 (plug in value of x)   

5 + 1 - 12 = 2 - 7 (did multiplication)   

-6 = -5 (did addition on both sides)       

since -6 is obviously not equal to -5, the value of 1 for x is wrong.