G A machine is designed to fill containers with 16 ounces of coffee. A consumer suspects that the machine is not filling the containers completely and the amount of coffee is less than 16 ounces when filled. A sample of 8 containers has a mean of 15.6 ounces of coffee and a standard deviation of 0.3 ounces of coffee. Assume that the distribution of data is normal. At 10% significance level, is there enough evidence to support the consumer’s suspicion that the machine is not filling the containers completely and the amount of coffee in a container is less than 16 ounces when filled?

The degrees of freedom are given by:

And the p value is given by this probability:

Since the p value is lower than the significance level provided of 0.1 we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly less than 16 ounces

Step-by-step explanation:

Information provided

represent the sample mean

represent the sample standard deviation

sample size  

represent the value to verify

represent the significance level

t would represent the statistic  

represent the p value

Hypothesis to test

We want to verify if amount of coffee in a container is less than 16 ounces when filled, the system of hypothesis would be:  

Null hypothesis:  

Alternative hypothesis:  

The statistic for this case would be given by:

 (1)  

Replacing the info given we got:

The degrees of freedom are given by:

And the p value is given by this probability:

Since the p value is lower than the significance level provided of 0.1 we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly less than 16 ounces

its 69.420

step-by-step explanation:

c. y = 1/4 x + 5

step-by-step explanation:

first, put the equation of the line on the graph into slope-intercept form

(y = mx + b):   y = -4x + 8

second, a perpendicular line has to have "an opposite/reciprocal slope" to the original slope. so, find the "m" value in your original equation (it's -4, right? )

original slope: m = -4   perpendicular slope: change the sign to its opposite and find the reciprocal ("flip" the number)

new slope is now positive (b/c the original slope was negative 4), and it's 1/4 (not the original slope of 4 or 4/1)