Question

1. This problem has 6 parts. This is part 1 of 6.

   A 2018 study by the USDA found that less than 20% of people do not wash their hands for at least 20 seconds, which is the CDC recommended amount of time. A healthcare professional believes that the COVID-19 outbreak has led to people being more diligent about handwashing, and that now this proportion has increased to greater than 20%. She designs a study and finds that 82 out of a random sample of 339 people wash their hands for the recommended amount of time.

   The healthcare professional claims, "the proportion of people who wash their hands for the recommended amount of time is greater than 20%." Select the pair of hypotheses that are appropriate for testing this claim.

   		H0: p ≤ 0.20 (claim) H1: p > 0.20
   		H0: p ≥ 0.20 (claim) H1: p < 0.20
   		H0: p ≥ 0.20 H1: p < 0.20 (claim)
   		H0: p < 0.20 (claim) H1: p ≥ 0.20
   		H0: p > 0.20 (claim) H1: p ≤ 0.20
   		H0: p > 0.20 H1: p ≤ 0.20 (claim)
   		H0: p ≤ 0.20 H1: p > 0.20 (claim)
   		H0: p < 0.20 H1: p ≥ 0.20 (claim)

2. Select the choice that best describes the nature and direction of a hypothesis test for this claim.

   		This is a right-tail t-test for p.
   		This is a two-tail z-test for p.
   		This is a right-tail z-test for p.
   		This is a left-tail z-test for p.
   		This is a left-tail t-test for p.
   		This is a two-tail t-test for p.

3. Find the standardized test statistic for this hypothesis test. Round your answer to 2 decimal places.

4. Find the P-value for this hypothesis test. Round your answer to 4 decimal places.

5. Using your previous calculations, select the correct decision for this hypothesis test.

   		Fail to reject the claim.
   		Reject the claim.
   		Fail to reject the null hypothesis.
   		Fail to reject the alternative hypothesis.
   		Reject the alternative hypothesis.
   		Reject the null hypothesis.

   6. Consider the following statements related to the healthcare professional's claim. Based on the results of your hypothesis test, which of these statements is true? Select the best choice.

   		The data is consistent with the healthcare professional's claim, but not enough to plausibly conclude that the proportion of people who wash their hands for the recommended amount of time is greater than 20%. We do not know if the healthcare professional is correct.
   		The data is not consistent with the healthcare professional's claim, but not enough to plausibly conclude that the proportion of people who wash their hands for the recommended amount of time is not greater than 20%. We do not know if the healthcare professional is incorrect.
   		The data is consistent with the healthcare professional's claim, enough to plausibly conclude that the proportion of people who wash their hands for the recommended amount of time is greater than 20%. The healthcare professional is likely to be correct.
   		The data is not consistent with the healthcare professional's claim, and we can plausibly conclude that the proportion of people who wash their hands for the recommended amount of time is not greater than 20%. The healthcare professional is likely to be incorrect.

Answer 1

The pair of hypotheses that are appropriate for testing this claim are as follows:

H0: p ≤ 0.20
H1: p > 0.20 (claim)

The nature and direction of a hypothesis test for this claim: This is a right-tail z-test for p.

Test statistic Calculation

Formula for test statistic is:

Here, p0 = 0.20, p̂ = 82/339 = 0.2419, n = 339

Test Statistic z = (0.2419-0.20)/sqrt(0.20*(1-0.20)/339)

z = 1.93

P-value Calculation

P-value corresponding to z = 1.93 for a right tailed test is obtained using p-value calculator.

P-value = 0.0269

Since p-value < 0.05, we reject the null hypothesis

Reject the null hypothesis

Conclusion

The data is consistent with the healthcare professional's claim, enough to plausibly conclude that the proportion of people who wash their hands for the recommended amount of time is greater than 20%. The healthcare professional is likely to be correct.