1. A national newspaper reported that 10% of Americans have received the vaccine for Covid-19 (as of February 10, 2021). A local community is concerned that their citizens are not being vaccinated at the same rate as the rest of the nation. In a random sample of 150 residents of this community, 8% have received the vaccine. Is there significant evidence that this community’s rate of vaccination is lower than the nation’s? Test an appropriate hypothesis and state your conclusion. (Make sure to check any necessary conditions and to state a conclusion in the context of the problem.) Ho: p = .1 Ha: p < .1 p-hat (sample proportion) = 0.08, n = 150 n*p-hat = 150*0.08 = 12 and n(1-p-hat) = 150*0.92 = 138 sample is random, sample size is less than 10 percent of the population 0.08-0.1/sqrt(0.1)(.9)/150 = -.82 Was your test one-tail upper tail, one-tail lower tail, or two-tail? Explain why you chose that kind of test in this situation. It was one tail lower tail, because we are trying to find whether the vaccination rate is lower than the national rate. Explain what your P-value means in this context. The value of P is larger than the significance level so we would have to fail to reject the null hypothesis. Therefore there is not sufficient enough evidence to suggest the community's vacation rate is lower than the national average.
Can someone tell me what I may have done wrong?
1. A national newspaper reported that 10% of Americans have received the vaccine for Covid-19 (as of February 10, 2021). A local community is concerned that their citizens are not being vaccinated at the same rate as the rest of the nation. In a random sample of 150 residents of this community, 8% have received the vaccine. Is there significant evidence that this community’s rate of vaccination is lower than the nation’s?
Test an appropriate hypothesis and state your conclusion. (Make sure to check any necessary conditions and to state a conclusion in the context of the problem.)
Ho: p = .1
Ha: p < .1
p-hat (sample proportion) = 0.08, n = 150
n*p-hat = 150*0.08 = 12 and n(1-p-hat) = 150*0.92 = 138
sample is random, sample size is less than 10 percent of the population
0.08-0.1/sqrt(0.1)(.9)/150 = -.82
Was your test one-tail upper tail, one-tail lower tail, or two-tail? Explain why you chose that kind of test in this situation.
It was one tail lower tail, because we are trying to find whether the vaccination rate is lower than the national rate.
Explain what your P-value means in this context.
The value of P is larger than the significance level so we would have to fail to reject the null hypothesis. Therefore there is not sufficient enough evidence to suggest the community's vacation rate is lower than the national average.
2. Allison wants to estimate the proportion of U.S. teens who think that a middle part is the best hairstyle. She chooses a random sample of 500 teenagers and finds that 64.8% believe a middle part is the best hairstyle.
Find a 90% confidence interval for the proportion of all U.S. teens who believe a middle part is the best hairstyle. Give an interpretation of the confidence interval and an interpretation of the confidence level.
Confidence intervals= .648 +/- 1.645 * sqrt (.648).352/500 = .63 and .67
An advocate for Ms. Timlin’s generation claims that only 60% of teenagers believe a middle part is best. Is this supported by Allison’s confidence interval?
60 percent does not lie between the confidence interval of 63% or 67%, the claim cannot be supported by the confidence interval at 90 percent.
If Allison wanted to be 99% confident instead, what would happen to the confidence interval?
Increasing the confidence level to 99 percent would increase the size of confidence interval
would increase because the z critical would be 2.58.
If Allison chose a sample size of 1000 instead, what would happen to the confidence interval?
If you were to double the sample size to 1000 it would decrease the size of the confidence interval because when you divide by a large number in computing the margin of error.
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