Question

Research question: In the population of all American adults, how strong is the relationship between age and reaction time? Data were collected from a representative sample of 500 American adults concerning their ages (in years) and reaction times (in milliseconds). What procedure should be used to estimate the strength of this relationship in the population? CI for single mean CI for single proportion CI for difference in means CI for difference in proportions CI for correlation

2Research question: To what extent do the GOALS scores of STAT 200 and STAT 500 students differ? A representative sample of students in each course took the GOALS. Scores ranged from 0 to 100. What procedure should be used to address this research question?

Question 3 When using the standard error method to construct a confidence interval, what is the point estimate?

4.When using the standard error method, what is the multiplier for a 95% confidence interval?

5.A researcher is using bootstrapping methods to estimate the mean IQ in the population of all students at one large university. What will the mean of his bootstrap sampling distribution be approximately equal to?

6.A statistician is using bootstrapping methods to construct a confidence interval to estimate a population proportion. The standard deviation of her bootstrap distribution is known as the of the proportion.

7.A representation sample of 1,000 American adults were surveyed and asked if they believe that regular exercise is important. Those data were used to construct a 95% confidence interval of [0.726, 0.779]. Select the correct interpretation of this confidence interval. We are 95% confident that the sample proportion is between 0.726 and 0.779. This confidence interval contains 95% of the data from the population. We are 95% confident that in the population of all American adults between 72.6% and 77.9% believe that regular exercise is important.

8.Data were collected from a representative sample of 70 male and 70 female students. Each student was asked how many hours per week they exercise. Researchers want to estimate the difference between the mean of the males and mean of the females (i.e., LaTeX: \mu_{male}-\mu_{female}μmale−μfemale). The 95% confidence interval is [0.59, 6.03]. Select the correct interpretation of this confidence interval. We are 95% confident that the difference between the mean number of hours exercised by males and females in this sample is between 0.59 hours and 6.03 hours. We are 95% confident that in the population of all students, the difference between the mean number of hours per week exercised by males and females is between 0.59 hours and 6.03 hours. In the population, 95% of males exercise more than 95% of females.

9.StatKey is used to construct a bootstrap sampling distribution to estimate a population correlation. That distribution is approximately normal with a mean of 0.420 and standard deviation of 0.096. Using the standard error method, construct a 95% confidence interval to estimate the correlation in the corresponding population. [0.324, 0.516] [0.228, 0.612] [0.132, 0.708] [0.036, 0.804] [-0.324, 0.516] [-0.744, 0.936]

10.We want to construct a 95% confidence interval to estimate the difference in two population means. We have a bootstrap distribution that is approximately normal with a mean of 9 and standard deviation of 3. Using the standard error method, what is the 95% confidence interval for the difference in population means? [0, 18] [4.5, 13.5] [6, 12] [3, 15]

11.A bootstrap sampling distribution for a mean was constructed with the following sample data: LaTeX: \overline x = 515x¯¯¯=515 LaTeX: s =100s=100 LaTeX: n=15n=15 The standard error was 25.822 in the bootstrap sampling distribution. If the sample size were increased to 500, how would the standard error change?

12.In a sample of 10 there were 6 success. StatKey was used to bootstrap a 95% confidence interval for the population proportion of [0.300, 0.900]. How would this confidence interval change if a sample size of 100, still with a 0.600 success rate, were obtained? It would be narrower It would not change It would be wider

13.In a sample of 20 one-bedroom apartments in Manhattan, the mean rent was $3156.50 per month with a standard deviation of $1372.07. Bootstrapping methods were used to construct a 95% confidence interval of [$2641.85, $3791.65]. How would this confidence interval be different if a sample size of 200, with similar sample statistics, were obtained? It would be narrower It would not change It would be wider

14.A survey of 1,000 randomly selected Centree County voters in November 2016 found that 48.8%, with a margin of error of 3%, identified as Republican. Given this information, is 50% a plausible value for the percentage of all Centree County voters who are Republican? Yes, 50% is a plausible population value No, 50% is not a plausible population value

15.A 95% confidence interval for the mean adult body temperature is [98.051, 98.480] in degrees Fahrenheit. Given this confidence interval, which of the following values are reasonable estimates of the population mean? Select all that are reasonable estimates. 97.895 98.000 98.120 98.380

Answer 1

Solution:-

14) Yes, 50% is a plausible population value.

The given confidence interval is (0.488 + 0.03) = ( 0.458, 0.518)

Since the given confidence interval contains 0.50, hence  50% is a plausible population value.

15) The reasonable estimates of the population mean are 98.266.

95% Confidence interval = [98.051, 98.480]