Problem 2 A study was conducted to see how long Dr. Kennedy’s patients had to wait...

Problem 2
A study was conducted to see how long Dr. Kennedy’s patients had to wait before their appointment. A random sample of 30 patients showed the average waiting time was 20 minutes with a standard deviation of 16 minutes.

(a) Construct a 99% conﬁdence interval for µ, the true mean waiting time and interpret your results.

(b) Suppose that Dr. Kennedy worker claims that the average waiting time at his hospital is 20 minutes. Based on the interval above, can this claim be rejected?

Solutions

Expert Solution

We need to construct the confidence interval for the population mean . Populaton standerd deviation is given hence One sample Z test is most appropriate here.
Confidence interval for Z test is given by:

where,
Sample Mean
Population Standard Deviation =
Sample size (n)=30

The critical value of Z at is

Therefore substituting the values we get C.I as:

b) Therefore, based on the data provided, the confidence interval for the population mean is which indicates that we are confident that the true population mean is contained by the interval (12.476, 27.524).
And the value 20 lies in this interval. Hence Dr. Kennedy worker's claims that the average waiting time at his hospital is 20 minutes can NOT be rejected

orchestra answered 1 year ago

Next > < Previous

Related Solutions

A survey was conducted to determine, on average, how long patients have to wait to see...

A survey was conducted to determine, on average, how long patients have to wait to see a doctor. The number of patients that ended up waiting up to 2 hours to see a doctor, recorded in 10-minute intervals, is given in the table below. a) Define and name the random variable associated with this data. b) Find the probability distribution for the random variable and draw the corresponding histogram. Express all probabilities as a fraction in lowest terms. c) What...

A study is to be conducted to see how long it takes for a taxpayer to...

A study is to be conducted to see how long it takes for a taxpayer to complete his income tax return. Assume that the time required to complete the return is normally distributed. A random sample of 17 taxpayers is taken whose mean (of the time in hours to complete the return) is 7.8 hours with a standard deviation of 2.3 hours. A) Determine the value of t B) Find the approximate error C) Find the interval with 95% confidence...

Problem 1 A study is conducted to investigate long-term complication rates in patients treated with two...

Problem 1 A study is conducted to investigate long-term complication rates in patients treated with two different therapies. The sample data is given below. Long-term complications Yes No Therapy 1 92 932 Therapy 2 75 878 Let p1 be the population proportion of patients with long-term complications among those treated with therapy 1. Let p2 be the population proportion of patients with long-term complications among those treated with therapy 2. Can we conclude that the proportions of patients with long-term...

Dr. Intellectual conducted a study to measure if a telephone intervention by nurses (nurses calling patients...

Dr. Intellectual conducted a study to measure if a telephone intervention by nurses (nurses calling patients after discharge) reduces readmissions within 30 days of discharge. All discharged patients were called within 48 hours of discharge, between June 1 and August 1, to discuss compliance with discharge instructions. 1. What type of research is this? a. qualitative b. quantitative 2. Which type of design is this? a. descriptive b. correlational c. quasi-experimental d. experimental e. phenomenological f. ethnography g. historical h....

Dr. Intellectual conducted a study to measure if a telephone intervention by nurses (nurses calling patients...

Dr. Intellectual conducted a study to measure if a telephone intervention by nurses (nurses calling patients after discharge) reduces readmissions within 30 days of discharge. All discharged patients were called within 48 hours of discharge, between June 1 and August 1, to discuss compliance with discharge instructions. 5. Identify the independent variable a. telephone calls b. readmissions c. 48 hours post discharge d. compliance with discharge instructions 6. What level of measurement is the independent variable?...

The length of time patients must wait to see a doctor in a local clinic is...

The length of time patients must wait to see a doctor in a local clinic is uniformly distributed between 15 and 45 minutes. a. Define the random variable in words. b. What is the probability of a patient waiting exactly 30 minutes? c. What is the probability that a patient would have to wait between 5 and 25 minutes? d. Compute the probability that a patient would have to wait over 30 minutes. e. Determine the expected waiting time and...

a)A sample of 25 patients in a doctor's office showed that they had to wait for...

a)A sample of 25 patients in a doctor's office showed that they had to wait for an average of 38 minutes before they could see the doctor. The sample standard deviation is 12 minutes. Assume the population of waiting times is normally distributed.At 95% confidence, compute the upper bound of interval estimate for the average waiting time of all the patients who visit this doctor. b)A sample of 30 patients in a doctor's office showed that they had to wait...

A sample of 36 patients in a doctor's office showed that they had to wait an...

A sample of 36 patients in a doctor's office showed that they had to wait an average of 45 minutes with a standard deviation of 12 minutes before they could see the doctor. Please provide a 95% confidence interval estimate for the average waiting time of all the patients who visit this doctor, and interpret your results (write a sentence explaining the results).

a) A sample of 25 patients in a doctor's office showed that they had to wait...

a) A sample of 25 patients in a doctor's office showed that they had to wait an average of 35 minutes before they could see the doctor. The sample standard deviation is 10 minutes. Assume the population of waiting times is normally distributed. At 95% confidence, compute the margin of error. b) A sample of 25 patients in a doctor's office showed that they had to wait for an average of 32 minutes before they could see the doctor. The...

a)A sample of 30 patients in a doctor's office showed that they had to wait an...

a)A sample of 30 patients in a doctor's office showed that they had to wait an average of 35 minutes before they could see the doctor. The sample standard deviation is 9 minutes. Assume the population of waiting times is normally distributed.At 90% confidence, compute the margin of error. b)Consider the population of electric usage per month for houses. The standard deviation of this population is 119 kilowatt-hours. What is the smallest sample size to provide a 90% confidence interval...

Subjects