Question

In: Statistics and Probability

A retirement planning firm conducted a survey of 80 working Americans and found that only 40%...

A retirement planning firm conducted a survey of 80 working Americans and found that only 40% of them had adequate retirement savings for their age group. Create the 99% confidence interval for the proportion of working Americans with adequate retirement savings.

Solutions

Expert Solution

Solution :

Given that,

n = 80

Point estimate = sample proportion = = 0.40

1 -   = 1- 0.40 =0.60

At 99% confidence level the z is ,

  = 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z/2 = Z0.005 = 2.576 ( Using z table )

Margin of error = E    Z/2 * (( * (1 - )) / n)

= 2.576*((0.40*0.60) /80 )

=0.1411

A99% confidence interval for population proportion p is ,

- E < p < + E

0.40-0.1411 < p < 0.40+0.1411

0.2589< p < 0.5411

The 909% confidence interval for the population proportion p is : 0.2589, 0.5411


Related Solutions

In the healthy handwashing survey, it was found the 64% of adult Americans operate the flusher...
In the healthy handwashing survey, it was found the 64% of adult Americans operate the flusher of toilets in public restrooms with their foot. Suppose you survey a random sample of 740 adult American women aged 18-24 years. Use normal approximation to the binomial to approximate the probability of following. a) check the conditions for normal distribution approximation c)determine probability of exactly 500 of those surveyed flush toilets in public restrooms with their foot. d) determine probability of no more...
Gallup recently conducted a survey about the proportion of Americans who use e-cigarettes (vape). The survey...
Gallup recently conducted a survey about the proportion of Americans who use e-cigarettes (vape). The survey data was collected via random-digit-dial telephone interviews conducted July 1-12, 2019 with a random sample of 1525 adults living in all 50 U.S. states with a minimum quota of 70% cellphone respondents and 30% landline respondents, with additional minimum quotas by time zone within region. The following table summarizes their results for men and women: Men Women Total Vape 92 31 123 Dont Vape...
Gallup recently conducted a survey about the proportion of Americans who use e-cigarettes (vape). The survey...
Gallup recently conducted a survey about the proportion of Americans who use e-cigarettes (vape). The survey data was collected via random-digit-dial telephone interviews conducted July 1-12, 2019 with a random sample of 1525 adults living in all 50 U.S. states with a minimum quota of 70% cellphone respondents and 30% landline respondents, with additional minimum quotas by time zone within region. The following table summarizes their results for men and women: Men Women Total Vape 92 31 123 Do Not...
In a survey conducted by the Fake Statistics Association, it was found that 125 of 200...
In a survey conducted by the Fake Statistics Association, it was found that 125 of 200 people in Texas approved of the current legislation on the economy. In a similar survey conducted in California, it was found that 210 out of 500 people approved of current economic legislation. Use this data to test the claim that the proportion of people in Texas who approve of the legislation is at least 7% higher than the proportion of people who approve it...
A Gallup poll to survey the top concerns of Americans was conducted. Suppose that 387 women...
A Gallup poll to survey the top concerns of Americans was conducted. Suppose that 387 women and 359 men were independently and randomly selected, and that 242 women and 202 men chose the state of the economy as their biggest concern. Can we conclude that the proportion of women (p1), choosing the state of the economy as their biggest concern, exceeds the proportion of men (p2)?  Use a significance level of α=0.01 for the test. Step 1: Choose the correct alternative...
A survey of 100 Americans found that 68% said they find it hard to buy holiday...
A survey of 100 Americans found that 68% said they find it hard to buy holiday gifts that convey their tr ue feelings. Find the 90% confidence interval of the population proportion.
(Hypothetical) In a major national survey of crime victimization, the researchers found that 17.0% of Americans...
(Hypothetical) In a major national survey of crime victimization, the researchers found that 17.0% of Americans age 12 or older had been a victim of crime. The size of the sample was 6,4,00. a) Estimate the percentage of Americans age 12 or older who were victims at the 95% confidence level. Write a sentence explaining the meaning of this confidence interval. b) Estimate the percentage of victims at the 99% confidence level. Write a sentence explaining the meaning of this...
In a recent survey conducted by Pew Research, it was found that 156 of 295 adult...
In a recent survey conducted by Pew Research, it was found that 156 of 295 adult Americans without a high school diploma were worried about having enough saved for retirement. Does the sample evidence suggest that a majority of adult Americans without a high school diploma are worried about having enough saved for retirement? Use a 0.05 level of significance. State the null and alternative hypothesis What type of hypothesis test is to be used? What distribution should be used...
A Pew Research study conducted in 2017 found that approximately 75% of Americans believe that robots...
A Pew Research study conducted in 2017 found that approximately 75% of Americans believe that robots and computers might one day do many of the jobs currently done by people.† Suppose we have the following data collected from nurses, tax auditors, and fast-food workers in which a higher score means the person feels his or her job is more likely to be automated. Nurse Tax Auditor Fast-Food Worker 4 4 6 5 5 7 5 4 6 2 3 8...
You are planning to save for retirement over the next 40 years. To do this, you...
You are planning to save for retirement over the next 40 years. To do this, you will invest $200 per month in a retirement account. The rate of return for the retirement account is expected to be 9 percent per year. After you retire, you expect that the account will have an annual return of 3 percent. How much can you withdraw each month from your account assuming a 25-year withdrawal period during retirement?
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT