#### MS 150 Statistics Fall 2001 Quiz Ten: In between 8 and 9

In math courses at the national campus Spring 2001 the campuswide population mean grade point average (GPA) µ was 1.613.  During the Spring 2001 term at the national campus 15 Yapese male students attained a sample mean GPA x of 1.133 with a standard deviation sx of 1.407 in math courses.  For a confidence level of 90%, is the Yapese male math GPA statistically significantly different than the national campus math GPA?

1. What is µ?

2. What is n?

3. What is x?

4. What is sx?

5. What is c?

6. How many degrees of freedom are there?

7. What is the tc critical value?

8. What is the error E?

9. Make a sketch of the confidence interval including:
a. the sample mean
b. the t-distribution curve
c. the critical values ±tc
d. the confidence interval
e. and the population mean µ.
Use the back if necessary to making a clean, clear, concise, legible, and accurate sketch.

10. Is the population mean within the 90% confidence interval for the Yapese male students sample mean?

11. Is the Yapese male student GPA statistically significantly below the campuswide math GPA for a confidence level of 90%?

Statistic or Parameter Symbol Equations Excel
Basic Statistics
Square root Ö =SQRT(number)
Sample size n =COUNT(data)
Sample mean x Sx/n =AVERAGE(data)
Sample standard deviation sx =STDEV(data)
Sample Coefficient of Variation CV 100(sx/x) =100*STDEV(data)/AVERAGE(data)
Normal Statistics
Calculate a z value from an x z = =STANDARDIZE(x, m, s)
Calculate an x value from a z x = s z + m = s*z+m
Calculate a z value from an x z
Calculate an x from a z =m + zc*sx/sqrt(n)
Find a probability p from a z value =NORMSDIST(z)
Find a z value from a probability p =NORMSINV(p)
Confidence interval statistics
Degrees of freedom df = n-1
Find a zc value from a confidence level c zc =ABS(NORMSINV((1-c)/2))
Find a tc value from a confidence level c tc =TINV(1-c,df)
Calculate an error tolerance E of a mean for n ³ 30 using sx E =zc*sx/SQRT(n)
Calculate an error tolerance E of a mean for n < 30 using sx. Can also be used for n ³ 30. E =tc*sx/SQRT(n)
Calculate a confidence interval for a population mean m from a sample mean x and an error tolerance E x-E< m <x+E
Hypothesis Testing
Calculate a t-statistic (tstat) t
Calculate t-critical for a two-tailed test tc =TINV(a,df)
Calculate t-critical for a one-tailed test tc =TINV(2*a,df)
Calculate a p-value from a t-statistic p = TDIST(ABS(tstat),df,#tails)