Module 7: Hypothesis Testing with One Sample

Null Hypothesis

• default assumption - no change, no difference, no effect - basically the opposite of what you want

Alternate Hypothesis

• What you want - the desired outcome/expectation

3 Forms of Alternative Hypothesis

1. Right tailed: mean(expectation) is higher/greater

2. Left tailed: mean(expectation) is lower/less than

3. Two tailed: mean(expectation) is different/not equal to

What does failing to reject the null value ACTUALLY mean?

• Failing the null doesn’t mean its true; we just don’t have enough evidence to prove the null hypothesis is false

P-value

the probability (after finding a test statistic: z-score or t-score)

p-vakue and null hypothesis: reject or not criterias

1. If P value is large, we fail to reject the null hypothesis

2. If P value is small (smaller than 0.05), we reject the null hypothesis

Type 1 Error

• “False Positive: Reject null hypothesis when it is in fact, TRUE

Type 2 Error

• “False Negative: Fail to reject null hypothesis when null hypothesis is actually FALSE

Significance Level

• the maximum probability of making a Type 1 Error that we’re willing to accept

What does lowering the significance level do but unadvertantly cause?

• lowering alpha (significance level, prob of making type 1 error) lowers chance of getting a Type 1 error but increases the chance of getting a Type 2 error instead

efffects of increasing and diecreasing alpha (Significance level) in terms of null hypothesis

• if increasing value of alpha, easier to reject null hypothesis

• if decreasing value of alpha, harder to reject null hypothesis

One Sample Z-test Conditions and Process

Conditions: The population SD is known, sample size is greater than or equal to 30

• Step 1: State the Hypothesis

• Step 2: Choose the significance level (usually given)

• Step 3: Perform the z test formula (as shown)

• Step 4: Find the p-value

• Step 5: Making a decision, interpret results: If p less than or equal to alpha, reject null. If p is greater than alpha, fail to reject null

The larger the z score, the…

More evidence it has to reject null hypothesis

One Sample T-Test Conditions and Process

Conditions: Use when population SD is unknown or is random, normal distributed

• Step 1: Generate/state null hypothesis and alternate hypothesis

• Step 2: Find/identify significance level

• Step 3: Use T formula for finding t value

• Step 4: Find the p value; ensure to use df = n-1

• Step 5: Compare result with the significance level

One Proportion Test: Conditions and Steps to use it

Conditions: Variables are categorical (yes/no, success/failure), TESTING A CLAIM ABOUT A POPULATION PROPORTION

• Step 1: Generate/State null hypothesis and alternate hypothesis

• Step 2: CHECK CONDITIONS BEFORE z test statistic and p value: sample is random, observations are independent, n x proportion AND n x (other than the proportion:q) are greater than or equal to 10

• Step 3: Find z value using normal z formula

• Step 4: Find p value

• Step 5: Conclude Results and Refer to Question