Question

A professor was interested in the average number of hours college students slept each night. A random sample of 23 college students found an average of 6.5 hours and a sample standard deviation of 1.5 hours. The professor wants to test the following hypotheses:_________-

Answer 1

Answer:

$t=\frac{6.5-7}{\frac{1.5}{\sqrt{23}}}=-1.599$    

Step-by-step explanation:

Assuming this complete question :"A professor was interested in the average number of hours college students slept each night. A random sample of 23 college students found an average of 6.5 hours and  a sample standard deviation of 1.5 hours. The professor wants to test the following hypotheses:

H0 :, Ha: $\mu <7$ Refer to Exhibit III. The test statistic is:"

Solution to the problem

Data given and notation    

$\bar X=6.5$ represent the sample mean

$s=1.5$ represent the sample standard deviation    

$n=23$ sample size    

$\mu_o =7$ represent the value that we want to test    

$\alpha$ represent the significance level for the hypothesis test.    

t would represent the statistic (variable of interest)    

$p_v$ represent the p value for the test (variable of interest)    

State the null and alternative hypotheses.    

We need to conduct a hypothesis in order to check if the mean is less than 7 :    

Null hypothesis:$\mu \geq 7$    

Alternative hypothesis:$\mu < 7$    

Since we don't know the population deviation, is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:    

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)    

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".    

Calculate the statistic    

We can replace in formula (1) the info given like this:    

$t=\frac{6.5-7}{\frac{1.5}{\sqrt{23}}}=-1.599$    

Now we can calculate the degrees of freedom:

$df=n-1=23-1=22$