Self-Reported Heights of Men (Example 18) A random sample of students at Oxnard College reported what they believed to be their heights in inches. Then the students measured each others’ heights in centimeters, without shoes. The data shown are for the men. Assume that the conditions for t -tests hold. a. Convert heights in inches to centimeters by multiplying inches by 2.54 . Find a 95 % confidence interval for the mean difference as measured in centimeters. Does it capture 0? What does that show? b. Perform a t -test to test the hypothesis that the means are not the same. Use a significance level of 0.05 , and show all four steps.
Self-Reported Heights of Men (Example 18) A random sample of students at Oxnard College reported what they believed to be their heights in inches. Then the students measured each others’ heights in centimeters, without shoes. The data shown are for the men. Assume that the conditions for t -tests hold. a. Convert heights in inches to centimeters by multiplying inches by 2.54 . Find a 95 % confidence interval for the mean difference as measured in centimeters. Does it capture 0? What does that show? b. Perform a t -test to test the hypothesis that the means are not the same. Use a significance level of 0.05 , and show all four steps.
Solution Summary: The author explains how to obtain the 95% confidence interval for mean differences using the MINITAB software.
Self-Reported Heights of Men (Example 18) A random sample of students at Oxnard College reported what they believed to be their heights in inches. Then the students measured each others’ heights in centimeters, without shoes. The data shown are for the men. Assume that the conditions for
t
-tests
hold.
a. Convert heights in inches to centimeters by multiplying inches by
2.54
. Find a
95
%
confidence interval for the mean difference as measured in centimeters. Does it capture 0? What does that show?
b. Perform a
t
-test
to test the hypothesis that the means are not the same. Use a significance level of
0.05
, and show all four steps.
Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...
Elementary StatisticsBase on the same given data uploaded in module 4, will you conclude that the number of bathroom of houses is a significant factor for house sellprice? I your answer is affirmative, you need to explain how the number of bathroom influences the house price, using a post hoc procedure. (Please treat number of bathrooms as a categorical variable in this analysis)Base on the same given data, conduct an analysis for the variable sellprice to see if sale price is influenced by living area. Summarize your finding including all regular steps (learned in this module) for your method. Also, will you conclude that larger house corresponding to higher price (justify)?Each question need to include a spss or sas output.
Instructions:
You have to use SAS or SPSS to perform appropriate procedure: ANOVA or Regression based on the project data (provided in the module 4) and research question in the project file. Attach the computer output of all key steps (number) quoted in…
Elementary StatsBase on the given data uploaded in module 4, change the variable sale price into two categories: abovethe mean price or not; and change the living area into two categories: above the median living area ornot ( your two group should have close number of houses in each group). Using the resulting variables,will you conclude that larger house corresponding to higher price?Note: Need computer output, Ho and Ha, P and decision. If p is small, you need to explain what type ofdependency (association) we have using an appropriate pair of percentages.
Please include how to use the data in SPSS and interpretation of data.
An environmental research team is studying the daily rainfall (in millimeters) in a region over 100 days.
The data is grouped into the following histogram bins:
Rainfall Range (mm) Frequency
0-9.9
15
10 19.9
25
20-29.9
30
30-39.9
20
||40-49.9
10
a) If a random day is selected, what is the probability that the rainfall was at least 20 mm but less than 40
mm?
b) Estimate the mean daily rainfall, assuming the rainfall in each bin is uniformly distributed and the
midpoint of each bin represents the average rainfall for that range.
c) Construct the cumulative frequency distribution and determine the rainfall level below which 75% of the
days fall.
d) Calculate the estimated variance and standard deviation of the daily rainfall based on the histogram data.
Probability And Statistical Inference (10th Edition)
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