1. A researcher wishes to estimate the proportion of left-handers among a certain population. In a...

1. A researcher wishes to estimate the proportion of left-handers among a certain population. In a random sample of 900 people from the population, 74% are left-handed.

a. Find the margin of error for the 95% confidence interval for the population proportion of the left-handers.

b. Find the 95% confidence interval for the population proportion of the left-handers to four decimal places.

Solutions

Expert Solution

Solution:

Given:

Sample size = n= 900

Sample proportion of left-handed =

Part a) Find the margin of error for the 95% confidence interval for the population proportion of the left-handers.

We need to find z_c value for c=95% confidence level.

Find Area = ( 1 + c ) / 2 = ( 1 + 0.95) /2 = 1.95 / 2 = 0.9750

Look in z table for Area = 0.9750 or its closest area and find z value.

Area = 0.9750 corresponds to 1.9 and 0.06 , thus z critical value = 1.96

That is : Z_c = 1.96

thus

Part b. Find the 95% confidence interval for the population proportion of the left-handers

orchestra answered 1 year ago

Next > < Previous

Related Solutions

A researcher at a major hospital wishes to estimate the proportion of the adult population of...

A researcher at a major hospital wishes to estimate the proportion of the adult population of the United States that has high blood pressure. How large a sample is needed to be 90% confident that the sample proportion will not differ from the true proportion by more than 5% A. If no preliminary estimate is available B. If a recent survey indicated that 43% of the population suffers from high blood pressure.

A researcher wishes to? estimate, with 99 ?% ?confidence, the population proportion of adults who are...

A researcher wishes to? estimate, with 99 ?% ?confidence, the population proportion of adults who are confident with their? country's banking system. His estimate must be accurate within 2 ?% of the population proportion. ?(a) No preliminary estimate is available. Find the minimum sample size needed. ?(b) Find the minimum sample size? needed, using a prior study that found that 36 ?% of the respondents said they are confident with their? country's banking system. ?(c) Compare the results from parts...

A researcher wishes to estimate, with 90% confidence, the population proportion of adults who think the...

A researcher wishes to estimate, with 90% confidence, the population proportion of adults who think the president of their country can control the price of gasoline. Her estimate must be accurate within 4% of the true proportion. a) No preliminary estimate is available. Find the minimum sample size needed. b) Find the minimum sample size needed, using a prior study that found that 32% of the respondents said they think their president can control the price of gasoline. c) Compare...

A researcher wishes to estimate, with 95% confidence, the population proportion of adults who are confident...

A researcher wishes to estimate, with 95% confidence, the population proportion of adults who are confident with their country's banking system. His estimate must be accurate within 4% of the population proportion. (a) No preliminary estimate is available. Find the minimum sample size needed. (b) Find the minimum sample size needed, using a prior study that found that 34% of the respondents said they are confident with their country's banking system. (c) Compare the results from parts (a) and (b)....

A researcher wishes to estimate, with 99% confidence, the population proportion of adults who are confident...

A researcher wishes to estimate, with 99% confidence, the population proportion of adults who are confident with their country's banking system. His estimate must be accurate within 4% of the population proportion. (a) No preliminary estimate is available. Find the minimum sample size needed. (b) Find the minimum sample size needed, using a prior study that found that 32% of the respondents said they are confident with their country's banking system. (c) Compare the results from parts (a) and...

A researcher wishes to estimate, with 95% confidence, the population proportion of adults who are confident...

A researcher wishes to estimate, with 95% confidence, the population proportion of adults who are confident with their country's banking system. His estimate must be accurate within 2% of the population proportion. (a) No preliminary estimate is available. Find the minimum sample size needed. (b) Find the minimum sample size needed, using a prior study that found that 22% of the respondents said they are confident with their country's banking system. (c) Compare the results from parts (a)...

A researcher wishes to estimate, with 90% confidence, the population proportion of adults who are confident...

A researcher wishes to estimate, with 90% confidence, the population proportion of adults who are confident with their country's banking system. His estimate must be accurate within 4% of the population proportion. (a) No preliminary estimate is available. Find the minimum sample size needed. (b) Find the minimum sample size needed, using a prior study that found that 32% of the respondents said they are confident with their country's banking system. (c) Compare the results from parts (a) and (b).

A researcher wishes to estimate, with 95% confidence, the population proportion of adults who think the...

A researcher wishes to estimate, with 95% confidence, the population proportion of adults who think the president of their country can control the price of gasoline. Her estimate must be accurate within 33% of the true proportion. a) No preliminary estimate is available. Find the minimum sample size needed. b) Find the minimum sample size needed, using a prior study that found that 3838% of the respondents said they think their president can control the price of gasoline. c) Compare...

A researcher wishes to estimate, with 95% confidence, the population proportion of adults who are confident...

A researcher wishes to estimate, with 95% confidence, the population proportion of adults who are confident with their country's banking system. His estimate must be accurate within 2% of the population proportion. (a) No preliminary estimate is available. Find the minimum sample size needed. (b) Find the minimum sample size needed, using a prior study that found that 22% of the respondents said they are confident with their country's banking system. (c) Compare the results from parts (a) and (b)....

A researcher wishes to estimate, with 95% confidence, the population proportion of adults who think the...

A researcher wishes to estimate, with 95% confidence, the population proportion of adults who think the president of their country can control the price of gasoline. Her estimate must be accurate within 44% of the true proportion. a) No preliminary estimate is available. Find the minimum sample size needed. b) Find the minimum sample size needed, using a prior study that found that 46% of the respondents said they think their president can control the price of gasoline. c) Compare...

Subjects