Question

Testing a claim about a proportion: In a sample random poll of 514 human resource professionals, 236 said that body piercings and tattoos were big grooming red flags. Use a 0.01 significance level to test the claim that less than 50 % of all human resource professionals say that piercings are big grooming red flags.

Show all of your 6 steps labeled in the box below.

Answer 1

Given that In a sample random poll of 514 human resource professionals, 236 said that body piercings and tattoos were big grooming red flags

So proportion, = 236 / 514

= 0.459144

Sample sizne n = 514

Step 1 :

Null Hypothesis H0 : p = 0.5

Alternate Hypothesis H1 : p < 0.5

where p is proportion of all human resource professionals who say that piercings are big grooming red flags

Step 2 :

Here we will use one proportion z-test since the sample size is greater than 30 and the test is left-tailed since we are looking for less than 50% here

Step 3 :

Level of significance = 0.01

Step 4 :

z-test statistic = ( - p) / p * (1 - p) / n

= (0.459144 - 0.5) / 0.5 * 0.5 / 514

= -0.040856 / 0.022054

= -1.852544

The p-value for a z-test statistic of -1.852544 for a left-tailed test is 0.031974

Step 5 :

If the p-value is less than the singificance level , we reject the Null Hypothesis H0 and conclude that there is enough evidence at given significance level to support the claim that the proportion of all human resource professionals who say that piercings are big grooming red flags is less than 50%

If the p-value is not less than the singificance level , we fail to reject the Null Hypothesis H0 and conclude that there is not enough evidence at given significance level to support the claim that the proportion of all human resource professionals who say that piercings are big grooming red flags is less than 50%

Step 6 :

Here the p-value of 0.031974 is not less than the singificance level of 0.01, Hence we fail to reject the Null Hypothesis H0 and conclude that there is not enough evidence at given significance level to support the claim that the proportion of all human resource professionals who say that piercings are big grooming red flags is less than 50%