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.
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;-
P1=11, p2=7, n1=n2=30
ṕ==0.6 , q= (1-ṕ)
Using a standard normal table to find P-value
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,
Zα /2 is the critical areaof α /2
P1-p2-E< (p1-p2) < (p1-p2) +E
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.
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.
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.
This is a two-tail test, and therefore Z-test for one population proportion can be used.
Critical value for a two tailed test Zc=1.96
Since the Z value is greater than Zc it can we can reject the null hypothesis.
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:
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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