Question

...Statistics students believe the mean grade on the first exam is 65. A statistics instructor thinks the mean grade is higher than 65. He samples ten statistics students and finds their mean grade is 67 with a standard deviation of 3.1972 for the sample. Use the Traditional Method and α = 0.05 to test the instructor’s claim. The data are assumed to be from a normal distribution. ...

State the information given:

State the claim in words:

State the claim in symbols:

State opposite if the claim is not true in symbols:

State the null and alternative hypothesis:

State alpha:

State the test statistic to use:

State the calculated value of the test statistic:

State the critical value of the test statistic:

Do you reject Ho? State why or why not.

State the conclusion as an English sentence.

Answer 1

From the sample of  ten statistics students sample mean grade is 67 with a standard deviation of 3.1972.

Here we want to test the claim by  statistics instructor that  the mean grade is higher than 65.

Let be the  the mean grade of statistics students.

Hence the null hypothesis is given as

i.e hypothesis of no difference., the  mean grade of statistics student is 65

The alternative hypothesis is given as

i.e  the mean grade of statistics students is higher than 65.

n=10

From the sample of ten statistics students

sample mean is

and sample standard deviation

s = 3.1972

The test statistic is given as

=  1.978155

Obtaining the critical value

df = n-1

= 9

The level of significance is

Decision rule :

Reject H0  if  

i.e if t( calculated) > t( critical value)

Since

we failed to reject the H0  .

The the mean grade is not significantly dfferent than 65, so the claim by  instructor is rejected.

Hence there is not sufficient evidence to conclude that the mean grade of statistics students is greater than 65.