Question

Complete steps 2 through 5 of the hypotheses test for the case study below. The hypotheses for step 1 are provided. Give the value of p rounded to the nearest ten-thousandth (to four decimal places). You can type H0 as Ho. A local produce supplier asserts that the average strawberry has fewer than 200 seeds. A sample of n = 10 strawberries had an average of x̅ = 185.2 seeds with a standard deviation of s = 19.7. Test the supplier’s claim at α = 0.05. H0: μ > 200 H1: μ < 200 (claim) ?

Complete steps 2 through 5 of the hypotheses test for the case study below. The hypotheses for step 1 are provided. Give the value of p rounded to the nearest ten-thousandth (to four decimal places). You can type H0 as Ho. An orthodontists advertises that his average price for teeth straightening is lower than the national average of $5400. For a random sample of n = 28 of his patients, the average price was x̅ = $5250 with a standard deviation of s = $629. Test the doctor’s claim at α = 0.10. H0: μ > 5400 H1: μ < 5400 (claim)?

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 200
Alternative Hypothesis, Ha: μ < 200

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (185.2 - 200)/(19.7/sqrt(10))
t = -2.376

P-value Approach
P-value = 0.0207

As P-value < 0.05, reject the null hypothesis.

2)

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 5400
Alternative Hypothesis, Ha: μ < 5400

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (5250 - 5400)/(629/sqrt(28))
t = -1.262

P-value Approach
P-value = 0.1089
As P-value >= 0.1, fail to reject null hypothesis.