Question

In: Statistics and Probability

In a random sample of 200 couples, the wife was taller than the husband in only...

In a random sample of 200 couples, the wife was taller than the husband in only 10 couples.

Construct a 99% confidence interval for the proportion of couples where the wife is taller

Solutions

Expert Solution

Solution :

Given that,

n = 200

x = 10

Point estimate = sample proportion = = x / n = 10/200=0.05

1 -   = 1- 0.05 =0.95

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* (((0.05*0.95) / 200)

E = 0.040

A 99% confidence interval for proportion p is ,

- E < p < + E

0.05-0.040 < p < 0.05+0.040

0.01 <p< 0.09

(0.01 , 0.09)


Related Solutions

In October of 2016, Jack and Judy, husband and wife, sold their (only) residence that they...
In October of 2016, Jack and Judy, husband and wife, sold their (only) residence that they had purchased in 1999 for $400,000 paying $300,000 in cash with a $100,000 mortgage from ABC Bank. They lived there the entire time they owned the home, and they made repairs to the electric and plumbing during their 10-year ownership totaling $40,000. What, if any, is their recognized gain or loss to be included on their jointly filed Form 1040 for 2017? a.      ...
​(​EBIT-EPS analysis​) Bill and Kate Theil are not only husband and wife but entrepreneurs who have...
​(​EBIT-EPS analysis​) Bill and Kate Theil are not only husband and wife but entrepreneurs who have established three successful businesses. The proposed plan for their latest effort involves a series of international retail outlets to distribute and service a full line of ingenious home garden tools. The stores would be located in​ high-traffic cities in Latin America such as Panama​ City, Bogotá,​ São Paulo, and Buenos Aires. The entrepreneurs have proposed two financing plans. Plan A is an all​ common-equity...
Only 4% of items produced by a machine are defective. A random sample of 200 items...
Only 4% of items produced by a machine are defective. A random sample of 200 items is selected and checked for defects. a. Refer to Exhibit 7-1. What is the expected value for ? b. What is the probability that the sample proportion will be within +/-0.03 of the population proportion c.What is the probability that the sample proportion will be between 0.04 and 0.07?
A husband and wife are planning for retirement and they believe that a comparison over a...
A husband and wife are planning for retirement and they believe that a comparison over a five- year period would be appropriate. They are given the following information about one mutual fund that they are considering. Assume that all remaining assets under management are withdrawn by the family at the end of 5 years.      Year Beginning Assets Under Management 30.000.000 35.000.000 25.000.000 15.000.000 20.000.000 Net Return (%) 1.   6% 2. 2% 3. -17% 4. -3% 5. 6% a. Compute...
A husband and wife are planning for retirement and they believe that a comparison over a...
A husband and wife are planning for retirement and they believe that a comparison over a five- year period would be appropriate. They are given the following information about one mutual fund that they are considering. Assume that all remaining assets under management are withdrawn by the family at the end of 5 years.      Year Beginning Assets Under Management 30.000.000 35.000.000 25.000.000 15.000.000 20.000.000 Net Return (%) 16% 12% -17% -3% 6% a. Compute the arithmetic and geometric mean...
Both the husband and wife have normal vision. The wife gives birth to a colour-blind daughter....
Both the husband and wife have normal vision. The wife gives birth to a colour-blind daughter. Is it more likely that the father is colour blind or has normal vision? What does this lead you to deduce about the girl’s parents genome?
Jamie and Cecilia Reyes are husband and wife and file a joint return. They live at...
Jamie and Cecilia Reyes are husband and wife and file a joint return. They live at 5677 Apple Cove Road, Boise, ID 83722. Jamie’s social security number is 412-34-5670 (date of birth 6/15/1967) and Cecilia’s is 412-34-5671 (date of birth 4/12/1969). They provide more than half of the support of their daughter, Carmen (age 23), social security number 412-34-5672 (date of birth 9/1/1993), who is a full-time veterinarian school student. Carmen received a $3,200 scholarship covering her room and board...
A husband and wife claim that they have a special bond that allows them to communicate...
A husband and wife claim that they have a special bond that allows them to communicate by ESP. To test this claim, an researcher puts the husband and wife in separate rooms. The husband is randomly shown one of 5 colors: either blue, red, green, yellow or orange. He then is given 5 seconds to use his ESP to communicate the color to his wife. The wife then has to decide which of the 5 colors she was shown. This...
Discuss the implications of both the abusive husband and the battered wife being patients of the...
Discuss the implications of both the abusive husband and the battered wife being patients of the practice.
Molly and Mark are wife and husband and earned salaries this year of $12,000 and $64,000,...
Molly and Mark are wife and husband and earned salaries this year of $12,000 and $64,000, respectively. In addition to their salaries, they received interest of $350 from municipal bonds and $500 from corporate bonds. Mark and Molly also paid $2,500 of qualifying moving expenses, and Marc paid alimony to a prior spouse in the amount of $1,500. Mark and Molly have a 10-year-old son, Matt, who lived with them throughout the entire year. Thus, Marc and Michelle are allowed...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT