Answer:
t48 = 1.7500
Step-by-step explanation:
A paired t-test is used to compare two population means where you have two samples in which observations in one sample can be paired with observations in the other sample. For example if we have Before-and-after observations (This problem) we can use it.
Let put some notation
x=test value before , y = test value after
The system of hypothesis for this case are:
Null hypothesis: 
Alternative hypothesis: 
We have the mean difference
And the sample standard deviation for the differences, is:
Now we can calculate the statistic given by :
Since we don't have the population standard deviaition we need to use the t distribution and we can calculate the degrees of freedom given by:
Now we can calculate the p value, since we have a right tailed test the p value is given by:
If we use a significance level of 5% we have that 
, and on this case we reject the null hypothesis
. And we don't have enough evidence to conclude that the difference of means it's higher than 50 points.
because of the distributive property and exponent laws.
If the average of the two integers is x, the product of the two integers is
(x-1)(x+1) = 440
x² - 1 = 440
x² = 441 = 21²
21 is the odd integer between the two even integers you seek.
The integers are 20 and 22.
Answer:
The number of single-shot espressos sold by the cafe was 49.
Step-by-step explanation:
It is provided that Addison's Cafe offers two kinds of espresso: single-shot and double-shot.
Total number of espressos sold by the cafe yesterday afternoon was,
<em>N</em> = 70
The proportion of single-shot espresso sold was, <em>p</em> = 0.70.
Let <em>X</em> = number of single-shot espressos sold.
Compute the number of single-shot espressos sold by the cafe as follows:
Thus, the number of single-shot espressos sold by the cafe was 49.
Answer:
118.25
Step-by-step explanation
If the tax is in percent, divide the tax rate by 100. You do this by moving the decimal point two spaces to the left. In this, there's 7.5/100 = 0.0
Find the tax value by multiplying tax rate by the item value:
tax = 110 × 0.075
tax = 8.25
