Question

In: Statistics and Probability

In an International Mass Retail Association survey of 1006 U.S. households, 324 of the households said...

In an International Mass Retail Association survey of 1006 U.S. households, 324 of the households said that Saturday is their favorite shopping day (USA Today, October 6, 1993). Construct a 95% confidence interval for the proportion of all U.S. households for whom Saturday is their favorite shopping day. Round your answer to three decimal places.

Expert Solution

Solution :

Given that,

n = 1006

x = 324

Point estimate = sample proportion = = x / n = 324/1006=0.322

1 - = 0.678

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96 ( Using z table )

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

= 1.96 ( $\sqrt$ ((0.322*0.678) /1006 )

E = 0.029

A 95% confidence interval is ,

- E < p < + E

0.322-0.029 < p < 0.322+0.029

0.293< p < 0.351

orchestra answered 1 year ago

According to a study by the American Pet Food Dealers Association, 63% of U.S. households own...

According to a study by the American Pet Food Dealers Association, 63% of U.S. households own pets. A report is being prepared for an editorial in the San Francisco Chronicle. As a part of the editorial, a random sample of 300 households showed 210 own pets. Do these data disagree with the Pet Food Dealers Association's data? Use a .05 level of significance. Why can you employ Z as the test statistic? State the null and alternate hypotheses. The decision...

According to the Consumer Electronics Manufacturers Association, 10% of all U.S households have a fax machine...

According to the Consumer Electronics Manufacturers Association, 10% of all U.S households have a fax machine and 52% have a personal computer. Suppose 91% of all U.S households having a fax machine also have a personal computer. a. What is the probability that a randomly selected US household has a fax machine and a personal computer? b. What is the probability that a randomly selected US household has a fax machine or personal computer? c. What is the probability that...

3. a. A survey of 1000 U.S. adults found that 34% of people said that they...

3. a. A survey of 1000 U.S. adults found that 34% of people said that they would get no work done on Cyber Monday since they would spend all day shopping online. Find the 90% confidence interval of the true proportion. ROUND TO FIVE DECIMAL PLACES b. In a recent year, 6% of cars sold had a manual transmission. A random sample of college students who owned cars revealed the following: out of 129 cars, 23 had manual transmissions. Estimate...

In a survey of 500 U.S. adults, 45% of them said that lounging at the beach...

In a survey of 500 U.S. adults, 45% of them said that lounging at the beach was their “dream vacation.’ Assuming this to be a simple random sample of U.S. adults, the lower confidence limit of the 95% confidence intervals for the proportion of U.S. adults who consider lounging at the beach to be their dream vacation would equal to;

In a survey of U.S. adults with a sample size of 2040, 315 said Franklin Roosevelt...

In a survey of U.S. adults with a sample size of 2040, 315 said Franklin Roosevelt was the best president since World War II. Two U.S. adults are selected at random from the population of all U.S. adults without replacement. Assuming the sample is representative of all U.S. adults, complete parts (a) through (d). (a) Find the probability that both adults say Franklin Roosevelt was the best president since World War II. The probability that both adults say Franklin Roosevelt...

a random survey of 1000 U.S. adults in 2007, 570 said it is likely that life...

a random survey of 1000 U.S. adults in 2007, 570 said it is likely that life exists on other planets. In a recent year, in a random survey of 1000 U.S. adults, 530 said it is likely that life exists on other planets. a) At a 5% level of significance, can you support the claim that the proportion of U.S. adults who believe it is likely that life exists on other planets is less now than in 2007? Hypotheses: Test...

1. In a survey of U.S. adults with a sample size of 2004, 345 said Franklin...

1. In a survey of U.S. adults with a sample size of 2004, 345 said Franklin Roosevelt was the best president since World War II. TwoTwo U.S. Two adults are selected at random from this sample without replacement. Complete parts (a) through (d). (a) Find the probability that both adults say Franklin Roosevelt was the best president since World War II. (b) Find the probability that neither adult says Franklin Roosevelt was the best president since World War II. (c)...

In a survey of 1118 U.S. adults conducted by the Financial Industry Regulatory Authority, 415 said...

In a survey of 1118 U.S. adults conducted by the Financial Industry Regulatory Authority, 415 said they always pay their credit cards in full each month. a) Construct a 95% interval for the population proportion of U.S. adults who pay their credit cards in full each month. To show work, write out the following: - The given numbers with their corresponding variables. - The formula that's used to calculate the confidence interval. Also give a short explanation stating why you...

According to a survey by the Association for Dressings and Sauces (this is a real association!),...

According to a survey by the Association for Dressings and Sauces (this is a real association!), 85% of American adults eat salad at least once a week. A nutritionist suspects that the percentage is lower than this. Conduct a survey of 200 American adults and discover that 160 of them eat salad at least once a week. Conduct a test that addresses the nutritionist's suspicions. Use a significance level of 0.10. Answer the following: Hypothesis test: Ho: p = Answer...

A marketing company survey found that, in the 100 households surveyed, in 65 households the women...

A marketing company survey found that, in the 100 households surveyed, in 65 households the women made the majority of the purchasing decisions. Find a 95% confidence interval for the proportion of households where women made the majority of purchasing decisions. Round your answer to the nearest hundredth.