For this assignment you MUST use the program Cocalc, otherwise the work will be incorrect 7.1
Math 151 Lab L Project 7
Due: April 4 at 11:59 pm.
Project 7 uses the R statistical language using the online CoCalc program to perform hypothesis tests. The following topics will be covered:
Use of the following R commands:
t.test()
Hypothesis Tests
A hypothesis test is a process that tests the validity of some claim being made about a population. The steps include:
Determine what the original claim is.
State the hypotheses:
Null Hypothesis (H0)
Alternate Hypothesis (H1 or HA)
The hypotheses states a population parameter and a value it is compared to. The null hypothesis will use the = operator (and sometimes <= and >=)
The alternate hypothesis will use the <, > and <> operators.
The operator used by the alternate hypothesis determines whether there will be a two-tailed test (<>), a left-tailed (one tail) test (<) or a right-tail (one tail) test (>).
Find a test statistic (z)
Use an appropriate formula or function to find the test statistic.
Find a critical value(s).
The critical value(s) are compared to the test statistic.
Use an appropriate formula and function to find the critical value(s).
Perform the test.
Compare the test statistic to the critical value(s):
If the test statistic falls within a critical region (the area preceding the critical value on the left side of a distribution and/or the area beyond the critical value on the right side of a distribution), reject the null hypothesis, else fail to reject the null hypothesis.
State the conclusion. The conclusion will state whether there is or is no evidence to support the original claim. Include the original claim in the conclusion.
7.2
Example:
For a data set containing a sample called x, test the claim that the population mean µ is 50, using a = 0.05.
Claim: µ = 50 Hypotheses:
H0: µ = 50
H1: µ <> 50
The alternate hypothesis contains <>, thus making this a 2-tailed test with two critical values. Find the test statistic.
For this example, assume the test statistic is +1.94. Find the critical values.
For a = 0.05, the critical values are -1.96 and +1.96. Compare the test statistic to the critical values:
The test statistic is neither less than the left critical value nor more than the right critical value; therefore, fail to reject the null hypothesis.
Conclusion:
There is no evidence to reject the claim that the µ of data x is 50.
Formulas
Test statistic z for mean (one large sample):
??¯ – ??
?? =
??/v??
Test statistic t for mean (one small sample):
??¯ – ??
?? =
??/v??
