MS 150 Statistics Summer 2001 Quiz Four: Sect 9.4

Name: _______________________________

In math courses at the national campus Spring 2001 the campuswide population mean grade point average (GPA) m was 1.613.  During the Spring 2001 term at the national campus 15 Yapese male students attained a sample mean GPA xbar.gif (842 bytes) of 1.133 with a standard deviation sx of 1.407 in math courses.  At an alpha a of 0.1, is the Yapese male math GPA statistically significantly lower than the national campus math GPA?

  1. What is Ho? 

  2. What is H1?

  3. What is alpha?

  4. Is this a one-tailed or a two-tailed test?

  5. What is the value of n?

  6. How many degrees of freedom are there?

  7. Calculate the t-statistic for the data.



  8. What is the tc critical value?



  9. Make a sketch of the student's t-distribution curve including the critical value for t, the critical area, and the t-statistic.  Use the back if necessary to making a clean, clear, concise, legible, and accurate sketch.





  10. Do we reject Ho or do we fail to reject Ho?


  11. Is the Yapese male student GPA statistically significantly below the campuswide math GPA at an alpha of 0.1?


 

Statistic Equations Excel
Square root =SQRT(number)
Sample size n =COUNT(data)
Sample mean xbar.gif (842 bytes) =AVERAGE(data)
Population mean m
x P(x)
n p (binomial)
=AVERAGE(data)
Sample standard deviation sx
sampstdev.gif (1072 bytes)
=STDEV(data)
Population standard deviation s
probabilitypopstdev.gif (1053 bytes)
npq.gif (927 bytes) (binomial)
=STDEVP(data)
Slope =SLOPE(y data, x data)
Intercept =INTERCEPT(y data, x data)
Correlation =CORREL(y data, x data)
Binomial probability = nCr pr q(n-r) =COMBIN(n,r)*p^r*q^(n-r)
Calculate a z value from an x z = standardize.gif (905 bytes) =STANDARDIZE(x, m, s)
Calculate an x value from a z x = s z + m
Calculate a z value from an xbar.gif (842 bytes) value given m and s xbartoz.gif (1022 bytes) =STANDARDIZE(x, m, s/SQRT(n))
Find a probability p from a z value =NORMSDIST(z)
Find a z value from a probability p =NORMSINV(p)
Standard error of the population mean standard_error_mean_sigma.gif (945 bytes)
Standard error of the sample mean standard_error_mean_sx.gif (956 bytes)
Determining z critical zc from a for confidence intervals or two-tail tests. =NORMSINV(1-a/2)
Error tolerance E of a mean for n ³ 30 using s error_tolerance_e.gif (987 bytes) =CONFIDENCE(a,s,n)
Error tolerance E of a mean for n ³ 30 using sx E = error_tolerance_zc.gif (989 bytes) =CONFIDENCE(a,sx,n)
Error tolerance E of a mean for n < 30.  Can also be used for n ³ 30. error_tolerance_tc.gif (989 bytes) [no Excel function, determine tc and then multiply by standard error of the mean as shown in the equation]
Determining tc from a and the degrees of freedom df for a confidence interval or a two-tail test. =TINV(a,df)
Calculate an xbar.gif (842 bytes) value from a tc xbar.gif (842 bytes)=error_tolerance_tc.gif (989 bytes)+ m
Calculate a confidence interval for a population mean m from a sample mean xbar.gif (842 bytes) and an error tolerance E xbar.gif (842 bytes)-E< m <xbar.gif (842 bytes)+E
Determining zc from a for a two-tail hypothesis test. =NORMSINV(a/2)
[returns only the negative value for zc]
Determining zc from a for a one-tail hypothesis test. =NORMSINV(a)
[returns the right tail zc, change the sign for the left tail]
Determining tc from a and degrees of freedom df for a two-tail hypothesis test. =TINV(a, df)
[returns only the positive value for tc]
Determining tc from a and degrees of freedom df for a one-tail hypothesis test. =TINV(2a, df)
[returns only the left-tail tc, change the sign for right-tail]
Determining the one-tail p-value for a z-statistic z for a negative value of z =NORMSDIST(z)
Determining the one-tail p-value for a z-statistic z for a positive value of z =NORMSDIST(1-z)
Determining the two-tail p-value for the absolute value of the z-statistic =2*NORMSDIST(1-|z|)
Determining the one-tail p-value for a t-statistic t and degrees of freedom df =TDIST(t,df,1)
[TDIST accepts only positive values for t, use the absolute value of t]
Determining the two-tail p-value for a t-statistic t and degrees of freedom df =TDIST(t,df,2)

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