What test should you use?

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~Note: Usually, in elementary statistics, we are mostly concerned with conjectures involving population means & population proportions. I will focus my discussion on these. There are other tests which examine data sets relative to "goodness of fit", "independence", "significant correlations", & so on. Some are described on this website under "Topics of Interest".
(See Chi-square & Correlation & Regression)

~Use a T-test (t-curves) for testing hypotheses involving MEANS where the population standard deviation is UNKNOWN. The following lists the steps involved on your TI-83:

(1) STAT
(2) TESTS
(3) menu 2, Enter
(4) enter DATA or STATS
(5) enter Null Hypothesis Mean (m₀)
(6) enter Sample Mean (X bar)
(7) enter Sample standard deviation (Sx)
(8) enter Sample size n
(9) Choose Alternate Hypothesis
(10) Calculate
(11) Enter

Displays shows: The alternate hypothesis, Test Statistic (t value), P-value, sample mean, sample standard deviation, & sample size. Reject the Null hypothesis if the P-value is less than the significance level (a).

~Use a Z-Test (the Standard Normal Curve) for testing Hypotheses involving MEANS where the population standard deviation is KNOWN.
The following lists the steps involved on your TI-83.

(1) STAT
(2) TESTS
(3) menu 1, Enter
(4) enter DATA or STATS
(5) enter Null Hypothesis Mean (m₀)
(6) enter Population standard deviation (s)
(7) enter Sample Mean (X bar)
(8) enter Sample size n
(9) Choose Alternate Hypothesis
(10) Calculate
(11) Enter

Displays shows: The alternate hypothesis, Test Statistic (z value), P-value, sample mean, & sample size. Reject the Null Hypothesis if the P-value is less than the significance level (a).

~Use the 1-PropZTest (the Standard Normal Curve) for testing hypotheses involving PROPORTIONS. The following lists the steps involved on your TI-83.

(1) STAT
(2) TESTS
(3) menu 5, Enter
(4) enter Null Hypothesis
(5) enter x number in sample (must be an integer)
(6) enter Sample size n
(7) Choose Alternate Hypothesis
(8) Calculate
(9) Enter

Displays shows: The alternate hypothesis, Test Statistic (z value), P-value, sample proportion (p cap), & sample size. Reject the Null Hypothesis if the P-value is less than the significance level (a).

~Note: Choose the appropriate alternate hypothesis for a right-tailed, left-tailed, or a two-tailed test.

(see Choosing the Alternate Hypothesis ).