Question

In: Statistics and Probability

it has been reported that 48% of people text and drive. A random sample of 60...

it has been reported that 48% of people text and drive. A random sample of 60 drivers is drawn. Find the probability that the proportion of people in the sample who text and drive is less than 0.498.

Expert Solution

Solution:

Given that,

n = 60

= 48% =0.48

1 - = 1 - 0.48 = 0.52

= = 0.48

= $\sqrt$ ( 1 - ) / n

= $\sqrt$ 0.48 * 0.52 / 60

= 0.0645

p ( < 0.498 )

p ( - / ) < ( 0.498 - 0.48 / 0.0645 )

p ( z < 0.018 / 0.0645 )

Using z table

p ( z < 0.28 )

= 0.6103

Probability = 0.6103

orchestra answered 1 year ago

It has been reported that 48% of teenagers play video games on their phones. A random...

It has been reported that 48% of teenagers play video games on their phones. A random sample of 60 teenages is drawn. Find the probability that the proportion of teenagers in the sample who play videos games on their phone is less than 0.500 . Write only a number as your answer. Round to 4 decimal places (for example 0.3748). Do not write as a percentage.

A proportion, p, of people who are alcoholics is 60%. A random sample of 130 people...

A proportion, p, of people who are alcoholics is 60%. A random sample of 130 people is done, and 63 of them confused to be an alcoholic. Can we reject the hypothesis that .05 level of significance? Show work.

In a random sample of 60 voters, 34 reported they voted for Candidate A and 26...

In a random sample of 60 voters, 34 reported they voted for Candidate A and 26 reported they voted for Candidate B. Let G denote a random variable equal 1 if the person voted for A and 0 if the person voted for B. (a) Find the sample average, ¯ G, and sample variance, S^2 G, of variable G. (b) Does Candidate A have more than 50% of the popular vote? Formulate and test the corresponding null and alternative hypotheses...

15. In a random sample of 60 adults, 55% of them reported having a fear of...

15. In a random sample of 60 adults, 55% of them reported having a fear of public speaking. (1)(1.5 points) Are the assumptions for constructing a confidence interval for the population proportion satisfied? Explain. (2)(5 points) Construct a 99% confidence interval for the population proportion of adults who have a fear of public speaking. (3)(2.5 points) Interpret the 99% confident interval. (4)(3.5 points) Estimate the sample size needed so that a 99% confidence interval will have a margin of error...

Question text In a random sample of 200 people, 32 people have blue eyes (characteristic B)....

Question text In a random sample of 200 people, 32 people have blue eyes (characteristic B). Which of the following 95% confidence intervals estimate the true proportion pp of measurements in the population with characteristic B? Select one: a. (0.109, 0.211) c. (0.431, 0.712) d. (0.561, 0.912)

In Mississippi, a random sample of 110 first graders revealed that 48 of them have been...

In Mississippi, a random sample of 110 first graders revealed that 48 of them have been to a dentist at least once. (a) Find a 95% confidence interval for the population proportion of first-graders in Mississippi who have been to a dentist at least once. Enter the smaller number in the first box. A poll is taken in which 367367 out of 600600 randomly selected voters indicated their preference for a certain candidate. Find a 8080% confidence interval for pp....

In a recent study of a random sample of 113 people, 92 reported dreaming in color....

In a recent study of a random sample of 113 people, 92 reported dreaming in color. In the 1940’s, the proportion of people who reported dreaming in color was 29%. Is there evidence to show that the proportion of people who dream in color is different than the proportion in the 1940’s? What is the p-value for this hypothesis test? What is the test statistic? What is the critical value? What is the decision? Options: A. 0.0380 B. 4145 C....

Suppose 48% of the population has a retirement account. If a random sample of size 632...

Suppose 48% of the population has a retirement account. If a random sample of size 632 is selected, what is the probability that the proportion of persons with a retirement account will differ from the population proportion by greater than 3%? Round your answer to four decimal places.

Question 6: From a random sample of 80 women, 48 say they have been sexually harassed....

Question 6: From a random sample of 80 women, 48 say they have been sexually harassed. From another random sample of 65 men, 13 say they have been sexually harassed. Construct a 95% confidence interval for the difference between the proportions of women and men who say they have been sexually harassed. If the problem is a confidence interval: Show whether the criteria for approximate normality are met. (1 point) Summarize the sample statistics. (1 point) Give the formula for...

A newspaper reported that 48% of smartphone purchases made by people with incomes between $35,000 to...

A newspaper reported that 48% of smartphone purchases made by people with incomes between $35,000 to $50,000 were a certain kind of phone. (a) If the story is based on a sample of 250 purchases, then should we conclude that this type of phone was getting less than half of the market at that time? (b) How large a sample is needed for the 95% confidence interval for the population proportion to exclude 50%? Please show and explain...