Answer to Question #210647 in Statistics and Probability for Dexter

Question

Activity 3: Discover Your Barangay: Decide for a situational problem you would

like to discover in your barangay, example, you claim that 75% preferred drinking

water during this time of pandemic rather than soft drinks. Make a survey by

deciding the number of respondents, you can asked them through messenger, text

or call for physical distancing during this time of pandemic, then formulate your

hypothesis and choose a significance level size for a. After having all the data needed,

show the complete step by step solution for the problem.

Answer 1

A random sample of 45 friends were asked to respond to the following question. Do you prefer drinking water during this time of pandemic rather than soft drinks? (Yes or NO). The data was coded where 0 represents NO and 1 represents Yes. Below are the collected data.

1 1 0 0 0 1 1 1 0 1 1 0 0 1 1 0 1 1 1 0 0 1 1 1 0 1 0 1 0 1 1 1 1 0 1 1 1 0 1 1 1 1 0 1 1

The claim is, 75% of people preferred drinking water during this time of pandemic rather than soft drinks. We want to use the sample proportion to test whether there is sufficient evidence to support the claim that the population proportion of those who prefer drinking water during this time of pandemic than soft drinks is 0.75.

Let x represent the number of successes (those who prefer drinking water than soft drinks).

$x=30$

$n=45$

$\hat {P}=\frac{30}{45}=0.667$

$P=0.75$

$H0:p=0.75$

$Ha:p\ne0.75$

$z=\frac{\hat{P}-P}{\sqrt{\frac{P(1-P)}{n}}}$

$z=\frac{0.667-0.75}{\sqrt{\frac{0.75\times0.25}{45}}}=-1.291$

Let $\alpha=0.05$

Thus, $z_{0.025}=1.96$

Since the test statistic (absolute value, 1.291) is less than the critical value (1.96), we fail to reject the null hypothesis. There is sufficient evidence to support the claim that 75% of people prefer drinking water during this time of pandemic rather than soft drinks.