Statistics Problems (RES 342)

Please help by providing solutions and SHOW WORK to help understand the set up for the problems. Distribution tables are attached for ease.
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1. In Week 1 of RES/342 we determined the optimal sample size, n, using a three variable formula. Fill in the following table listing the three variables and specify the effect on n (either + or -) of increasing and decreasing each variable, one at a time.
VARIABLE EFFECT of INCREASE EFFECT of DECREASE

2. Given a Chi-Square problem where the sum of the observed frequencies (first column) is 500, the sum of the expected frequencies (second column) should equal _________and the sum of the observed frequencies minus the expected frequencies (third column) should equal _________.

3. Given a two-tailed hypothesis test where n = 40, the desired level of confidence is 95% and the population standard deviation is known, we would use the ______ test for the ______ level of significance and the critical value of __________.

4. Given an upper tail hypothesis test where n = 25, the desired level of confidence is 90% and the population standard deviation is unknown, we would use the ______ test for the ______ level of significance and the critical value of __________.

5. If the value of the test statistic falls in the "rejection region", our data are inconsistent with _______ and the decision should be to accept the _____________.

6. Degrees of freedom in a Chi-Square problem is dependent upon the number of _____________ while degrees of freedom in an F Distribution problem is dependent on _____________ in both the ___________________ and the _____________________.

7. Please fill in the second table given a 0.05 level of significance and the following data:
ROUTE MEAN TIME STANDARD DEVIATION OBSERVATIONS
Freeway 40 minutes 3 minutes 12 commuters
Surface Streets 45 minutes 5 minutes 8 commuters

Numerator Denominator Degrees of Freedom Numerator Degrees of Freedom Denominator F Critical Value Factor(s) & Levels Response Variable