Men are less likely to wear masks in public than women.

To determine a claim that men are less likely to wear masks in public than women. I interviewed a random sample of 30 men and 30 women.In a random sample of 30 men, 11 agreed that they are less likely to wear a mask, while in a random sample of 30 women, 7 of them agreed that they are less likely to wear masks.

  Yes No
Men 11 19
Women 7 23

 

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Let the first sample n1 be the sample size of men, and the second n2 be the sample size of women. The success x is defined as the number of people who agreed that they are less likely to wear a mask. The two-sample proportion is from independent and random samples. I used a 0.05 significance level, and the results are as follows;-

 

Hypothesis

Ho: p1=p2

H1:p1>p2

P1=11, p2=7, n1=n2=30

P1==0.3667 p2==0.2333

ṕ==0.6    , q= (1-ṕ)

Z=

Z=1.127

Using a standard normal table to find P-value

P-value =0.1299

So the P-value is greater than the significance level of α 0.05; therefore, we accept the null hypothesis since there is not enough evidence to support the claim. These results suggest that men are equally likely to wear masks in public as women. P-value is 0.130, which means that if H0 is rejected, the type I error will be high, at 13%.

Constructing a 95% confidence interval to estimate the difference between p1 and p2. The inequality E is the margin of error obtained by the following formula,

 

E=Zα /2

Zα /2 is the critical areaof α /2

P1-p2-E< (p1-p2) < (p1-p2) +E

-0.096<p1-p2) <0.363

 

Since the confidence interval includes zero, there is not enough evidence suggesting that men are less likely to wear masks than females; therefore, we do not have sufficient evidence to reject the null hypothesis.

It can be represented in the graph below.

 

Quantitative Data

Further, to determine the effect of Covid-19, I interviewed a random sample of 30 people to investigate a claim that the unemployment rate has increased by 11%due to the impact of Covid-19.

Sample size Yes No
30 8 21

 

Among the 30 random samples,8 of them said they had lost their job due to the disease’s impact.I used a 0.05 significance level.

The hypothesis to be tested.

H0: p=0.11

H1:p≠ 0.11

This is a two-tail test, and therefore Z-test for one population proportion can be used.

P===0.2667

n =30

α= 0.05

Critical value for a two tailed test Zc=1.96

Z=

=

Z​=2.742

Since the Z value is greater than Zc it can we can reject the null hypothesis.

P-value=0.0061

We can also use P-value, where P-value-0.0061which is less than the significance level α= 0.05; therefore, we reject the null hypothesis since there is enough evidence to support the claim.

95% confidence interval on the mean:

[0.108, 0.425]

The confidence interval shows that 95% of the unemployment rate due to covid-19 lies between 10.8% and 42.5%.

 

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