Question

A study was conducted regarding the wearing of masks by the public during the COVID 19 reopening. They surveyed 900 people to see whether the people were complying with the mask-wearing guidelines. The researchers used 85% as an assumed proportion of compliance but hoped there would be evidence to suggest the proportion of people in compliance is higher than 85%. So, the hypotheses are given below.

H0:p=0.85,      Ha:p>0.85

For the different sample proportions given below, label them as either: (note, one should be A, one should be B and one should be C)

1. Providing no evidence against the null hypothesis and in support of the alternative hypothesis.
2. Providing some evidence, but not a lot of evidence, against the null hypothesis and in support of the alternative hypothesis.
3. Providing STRONG evidence against the null hypothesis and in support of the alternative hypothesis.

1.)  p=0.89

2.) p=0.844   

3.) p=0.86   

Answer 1

1) H₀: p = 0.85

    H_a: p > 0.85

The test statistic is

   

  

P-value = P(Z > 3.36)

             = 1 - P(Z < 3.36)

             = 1 - 0.9996

             = 0.0004

Since the P-value is very small, so we should reject H₀.

Option - C) Providing STRONG evidence against the null hypothesis and in support of the alternative hypothesis.

2) H₀: p = 0.85

    H_a: p > 0.85

The test statistic is

   

  

P-value = P(Z > -0.50)

             = 1 - P(Z < -0.50)

             = 1 - 0.3085

             = 0.6915

Since the P-value is larger, so we should not reject H₀.

Option - A) Providing no evidence against the null hypothesis and in support of the alternative hypothesis.

3) H₀: p = 0.85

    H_a: p > 0.85

The test statistic is

   

  

P-value = P(Z > 0.84)

             = 1 - P(Z < 0.84)

             = 1 - 0.7995

             = 0.2005

Since the P-value is greater, so we should not reject H₀.

Option - A) Providing some evidence, but not a lot of evidence, against the null hypothesis and in support of the alternative hypothesis.