Question

In: Math

A systematic random sample was taken from the set of all Presidents of the United States....

A systematic random sample was taken from the set of all Presidents of the United States. The data file potus heights.csv random sample includes the height (in inches) of each sampled President. (a) From this data, estimate the average height of United States Presidents. Calculate two error bounds for your estimate, one using the usual SRS formula, and one using the successive difference variance estimator. (b) Which variance estimator is more appropriate for these data? Briefly explain

president	hgt
Van Buren	56
McKinley	57
Harrison	68
Carter	69
Roosevelt	70
Cleveland	71
Buchanan	72
Kennedy	72
AJackson	73
GHWBush	74
Lincoln	76

Expert Solution

president

hgt

Van Buren

56

McKinley

57

Harrison

68

Carter

69

Roosevelt

70

Cleveland

71

Buchanan

72

Kennedy

72

Ajackson

73

GHWBush

74

Lincoln

76

Average height of United states president=

68.90909

variance=

38.80992

Standard deviation=

6.229761

using normality asumption for simple srs we can compute error bounds

(68.9090-6.2297/sqrt(11))*1.96)

and

(68.9090+(6.2297/sqrt(11))*1.96)

65.22748

and

72.59052

at 5% los

method 2

successive difference variance method

variance =

(1-1/n)*σ² =

35.28175

and

STANDARD Deviation=

5.939844

using normality asumption we can obtain bounds

(68.9090-(5.9398/sqrt(11))*1.96)

and

(68.9090+(5.9398/sqrt(11))*1.96)

65.3988

and

72.4192

at 5% los

b) successive difference variance estimator is more appropriate for this data

milcah answered 8 months ago

3. A random sample of wolf dens in the southwestern United States is taken. The number...

3. A random sample of wolf dens in the southwestern United States is taken. The number of pups found are: 5 8 7 5 3 4 3 9 5 8 5 6 5 6 4 7 a. Find a 90% confidence interval for the population mean number of wolf pups per den. Include the sample statistics, degrees of freedom, LaTeX: t_{\frac{\alpha}{2}}t α 2 , standard error and a sentence. b. What sample size is needed for the margin of error...

The data below is a random sample of 3 observations drawn from the United States population....

The data below is a random sample of 3 observations drawn from the United States population. Use the data to answer the following questions i. Find 95% confidence intervals of the population mean of experience and wage. ii. Estimate ρe,w, the correlation between the variables experience and wage. iii. Find βˆ 1 and βˆ 0, the estimates of the parameters in the following regression equation wage = β0 + β1education + ϵ iv. Predict wages for a person with 15...

The ages of some vice presidents in the United States at the time of their death...

The ages of some vice presidents in the United States at the time of their death are listed below. 50 62 65 71 79 51 64 67 76 86 54 65 68 77 87 1. Construct a group frequency distribution using 4 classes. class limits, class boundaries, frequency and relative frequency 2. Construct a cumulative frequency distribution with the ages of some vice presidents at the time of their death. Class boundaries, cumulative frequency and cumulative relative frequency

A simple random sample of 101 cities and counties in the United States was selected and...

A simple random sample of 101 cities and counties in the United States was selected and the number of positive COVID-19 cases per 1000 citizens was recorded for each. The mean number of positive cases for this sample of 101 counties and cities was 253, with a standard deviation of 11.4. Due to a couple of cities with extremely high numbers of cases the distribution is skewed heavily to the right. If appropriate, use this information to calculate and interpret...

A simple random sample of birth weights in the United States has a mean of...

A simple random sample of birth weights in the United States has a mean of 3433g. The standard deviation of all birth weights (for the population) is 495g. If this data came from a sample size of 75, construct a 95% confidence interval estimate of the mean birth weight in the United States. If this data came from a sample size of 7,500, construct a 95% confidence interval estimate of the mean birth weight in the United States. Which...

In a random sample of 765 adults in the United States, 322 say they could not...

In a random sample of 765 adults in the United States, 322 say they could not cover a $400 unexpected expense without borrowing money or going into debt. A.)Find the mean and the standard deviation of p-hat for this sample B.) Given the sample data in problem (1) above, construct a confidence interval at the 95% confidence level for the true proportion of Americans who could not cover a $400 unexpected expense without borrowing money or going into debt. C.)4)...

A random sample of 25 workers showed that the average workweek in the United States is...

A random sample of 25 workers showed that the average workweek in the United States is down to only 35 hours, largely because of a rise in part-time workers. The variance of the sample was 18.49 hours. Assuming that the population is normally distributed, calculate a 98% confidence interval for the population standard deviation.

Consider the sample space of all people living in the United States, and within that sample...

Consider the sample space of all people living in the United States, and within that sample space, the following two events. ??=people who are college graduates=people who are unemployedA=people who are college graduatesB=people who are unemployed Suppose the following statements describe probabilities regarding these two events. Which of the statements describe conditional probabilities? Select all that apply. The probability is 4.1% that a college graduate is unemployed. Twenty‑six point two percent of unemployed people are college graduates. There is a...

1. A random sample of 2,500 students is taken from the population of all part-time students...

1. A random sample of 2,500 students is taken from the population of all part-time students in the United States, for which the overall proportion of females is 0.6. There is a 95% chance that the sample proportion (p̂) falls between ______ and _______. 2. The Federal Pell Grant Program provides need-based grants to low-income undergraduate and certain postbaccalaureate students to promote access to postsecondary education. According to the National Postsecondary Student Aid Study conducted by the U.S. Department of...

. A bank has taken a random sample of 4 customers for each set of various...

. A bank has taken a random sample of 4 customers for each set of various criteria to determine their level of customer satisfaction on a scale of 0 to 10. The data appear in the table below. (20 points) Factor 1: Factor 2: Type of contact Time of day Automated Bank Representative Row means Morning 6, 5, 8, 4 8, 7, 9, 9 Row 1 ? = 5.75 ? = 8.25 ? = 7.00 Afternoon 3, 5, 6, 5...