Aim: How do we use a t-test? Exam Friday HW: complete worksheet

Recap: z-test Use a z-test when sample size is 30 or more

Example A researcher claims that the average wind speed in a certain city is 8 miles per hour. A sample of 32 days has an average wind speed of 8.2 miles per hour. The standard deviation of the sample is 0.6 mile per hour. At α=0.05, is there enough evidence to reject the claim? Use the P-value method.

Example Solution Step 1: State the hypotheses and identify the claim Step 2: Compute the test value Step 3: Find the P-value (from z-table) – area under the curve Step 4: Make the decision Since the P-value is greater than 0.05, the decision is not to rejected the null hypothesis; therefore we ACCEPT the null hypothesis Step 5: Summarize Results There is not enough evidence to reject the claim that the average wind speed is 8 miles per hour.

Drawing the Curve

Decision Rule when using P-values If P-value ≤ α, reject the null hypothesis. If P-value > α do not reject the null hypothesis.

T-test T-test: a statistical test for the mean of a population and is used when the population is normally or approximately normally distributed and n < 30. The formula for the t test is The degree of freedom are d.f. = n - 1

Simple Example: Using Table F Find the critical t value of α = 0.05 with d.f. = 16 for a right tailed t test. Solution: Find the 0.05 column in the top row and 16 in the left-hand column. Where the row and column meet, the appropriate critical value is found It is +1.746

Hypothesis Testing With T-Test A job placement director claims that the average starting salary for nurses is $24,000. A sample of 10 nurses’ salaries has a mean of $23,450 and a standard deviation of $400. Is there enough evidence to reject the director’s claim at α=0.05?

Solution Step 1: State null and alternative hypothesis Step 2: Find critical values - d.f. = 9, two tailed, α = 0.05, table F - critical values = ±2.262 Step 3: Find test value Step 4: Make a decision - reject the null hypothesis since -4.35 < -2.262 Step 5: Summaries - There is not enough evidence to reject the claim that the starting salary of nurses is $24,000.

When to use what test? If sample standard deviation is known, use the z-test. The variable must be normally distributed if n < 30. If sample standard deviation is unknown but n ≥ 30, use the z test and use population standard deviation in formula. If sample standard deviation is unknown and n<30, use the t test. (The population must be approximately normally distributed.)

Class Work 8 Worksheet Must be handed in at the end of the period NO LATE ASSIGNMENTS WILL BE ACCEPTED!