More Hypothesis Test Examples

More Hypothesis Test Examples

Solve the following:

The standard deviation of human body temperatures is equal to 0.62⁰F

Now, express the null hypothesis H0 and alternative hypothesis H1 in symbolic form.

Be sure to use the correct symbols (µ= mean, p= proportion, and σ=standard deviation) for the indicated parameter.

ANSWER: The standard deviation is represented by the symbol σ, so we get the following hypotheses:

Ho: σ = 0.62⁰

H1: σ ≠ 0.62⁰

Example 1:

Test the claim about the population mean µ at the given level of significance using the given sample statistics.

Claim: µ = 40; α = 0.05. Sample statistics x = 39.2, s = 3.23, n = 75

Remember that the statement of equality (=) goes in the null hypothesis. If the statement has ≠, <, > then it goes in the alternative hypothesis.

Our claim is given to be µ = 40. Remember that only the null hypothesis contains equality, so in this case our claim will be that the null hypothesis is true. So our Hypotheses are:

H0 : µ = 40

Ha: µ ≠ 40

If we use the p-value method (see page 414, 428), we first notice that we have a two tailed test (since the alternative hypothesis has a ≠ ). Then since α=.05, we will compare our p-value to ½ α=.025 on each tail.

So we first need to find the statistic and p-value and compare it to ½ α=.025; if the p-value is less than 0.025 then we Reject Ho, and if it is greater than 0.025 then we Fail to Reject Ho. Try to remember "if the p is low, Ho has gotta go" (i.e. reject Ho).

So next let's calculate our sample statistic for the mean. See page 411.

z = (x- µ)/(s/√n) = (39.2-40)/ (3.23/√75) = -0.8/0.373 ≈ -2.145

Now let's calculate the p-value = P(z< -2.145), we can use our Table or the Excel Function, NORMSDIST(-2.145) = 0.016. Since our p-value =0.016 < 0.025, then we Reject Ho. Since Ho was our claim, there is enough evidence to reject our claim.

Example 2:

The claim is µ < 8000. Remember that if the statement of equality (=) goes in the null hypothesis. If the statement has ≠, <, > then it goes in the alternative hypothesis.

H0 : µ = 8000

Ha: µ < 8000

Note: