A Bernoulli trial is repeated 525 times and the number of successes observed is 96. At...

A Bernoulli trial is repeated 525 times and the number of successes observed is 96.

At a confidence level of 97%, calculate the margin of error in the estimated proportion of successes.

Solutions

Expert Solution

Solution :

Given that,

n = 525

x = 96

Point estimate = sample proportion = = x / n = 96/525=0.183

1 - = 1-0.183 =0.817

At 97% confidence level the z is ,

= 1 - 97% = 1 - 0.97 = 0.03

/ 2 = 0.03 / 2 = 0.015

Z/2 = Z0.015 = 2.170 ( Using z table )

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

= 2.170 ( $\sqrt$ ((0.183*0.817) / 525)

= 0.0366

At a confidence level of 97%, calculate the margin of error in the estimated proportion of successes. is 0.0366

orchestra answered 2 years ago

Next > < Previous

Related Solutions

We observed 28 successes in 70 independent Bernoulli trials. Compute a 90% confidence interval for the...

We observed 28 successes in 70 independent Bernoulli trials. Compute a 90% confidence interval for the population proportion p.

Let the probability of success on a Bernoulli trial be 0.20. a. In nine Bernoulli trials,...

Let the probability of success on a Bernoulli trial be 0.20. a. In nine Bernoulli trials, what is the probability that there will be 8 failures? (Round your final answers to 4 decimal places.) Probability b. In nine Bernoulli trials, what is the probability that there will be more than the expected number of failures? (Round your final answers to 4 decimal places.) Probability

Assume that a procedure yields a binomial distribution with a trial repeated n=5n=5 times. Use some...

Assume that a procedure yields a binomial distribution with a trial repeated n=5n=5 times. Use some form of technology like Excel or StatDisk to find the probability distribution given the probability p=0.533p=0.533 of success on a single trial. (Report answers accurate to 4 decimal places.) k P(X = k) 0 1 2 3 4 5

13. Assume that a procedure yields a binomial distribution with a trial repeated n=5n=5 times. Use...

13. Assume that a procedure yields a binomial distribution with a trial repeated n=5n=5 times. Use some form of technology to find the cumulative probability distribution given the probability p=0.155p=0.155 of success on a single trial. (Report answers accurate to 4 decimal places.) k P(X < k) 0 1 2 3 4 5

The number of times a machine broke down each week was observed over a period of...

The number of times a machine broke down each week was observed over a period of 100 weeks and recorded as shown in the table below. Complete parts a and b below. Number of Breakdowns 0 1 2 3 4 5 or More Number of weeks 9 22 32 26 6 5 a. Using alphaequals?0.10, perform a? chi-square test to determine if the population distribution of breakdowns follows the Poisson probability distribution. What is the null? hypothesis, Upper H 0??...

Bernoulli Trials. Probability is 0.26 Calculate the probability of 4 successes in 4 tries. (Please show...

Bernoulli Trials. Probability is 0.26 Calculate the probability of 4 successes in 4 tries. (Please show work)

A coin is flipped 34 times and heads is observed 22 times. Assuming this proportion is...

A coin is flipped 34 times and heads is observed 22 times. Assuming this proportion is normal for this particular coin, if the coin is flipped 50 times, what is the probability that heads is observed at least 25 times? The probability is: (Round to 4 decimal places)

Seventy-one successes were observed in a random sample of n = 120 observations from a binomial...

Seventy-one successes were observed in a random sample of n = 120 observations from a binomial population. You wish to show that p > 0.5. State the null and alternative hypothesis. H0: p ≠ 0.5 versus Ha: p = 0.5H0: p < 0.5 versus Ha: p > 0.5 H0: p = 0.5 versus Ha: p ≠ 0.5H0: p = 0.5 versus Ha: p > 0.5H0: p = 0.5 versus Ha: p < 0.5 Calculate the appropriate test statistic. (Round your answer...

The number of successes and the sample size are given for a simple random sample from...

The number of successes and the sample size are given for a simple random sample from a population. Use the one-proportion z-interval procedure to find the required confidence interval. n = 76, x = 31; 98% level 0.298 to 0.518 0.276 to 0.540 0.297 to 0.519 0.277 to 0.539 Use the one-proportion z-interval procedure to find the required confidence interval. A researcher wishes to estimate the proportion of adults in the city of Darby who are vegetarian. In a random...

The following table contains the number of successes and failures for three categories of a variable....

The following table contains the number of successes and failures for three categories of a variable. Test whether the proportions are equal for each category at the α=0.1 level of significance. Category 1 Category 2 Category 3 Failures 70 76 52 Successes 58 52 71 State the hypotheses. Choose the correct answer below. A. H0: The categories of the variable and success and failure are dependent. H1: The categories of the variable and success and failure are independent. B. H0:...

Subjects