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Statistical Sciences 1024A/B Chapter Notes - Chapter 20: Simple Random Sample, Test Statistic, Normal Distribution

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School
Western University
Department
Statistical Sciences
Course
Statistical Sciences 1024A/B
Professor
Sohail Khan

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Document Summary

If these conditions are satisfied: sampling distribution of x is normal with mean and standard deviation n. Standard error of the mean (semean) when the standard deviation of a statistic is: varies from sample to sample, therefore standard error also varies from sample estimated from data to sample. The one-sample t statistic and the t distributions. Take an srs from a large population with a normal distribution with and. However, when performing inference, is almost always unknown. A t distribution is specified by its degrees of freedom: n 1. In general, df = amount of sample info for estimating. T-table: one-sided p shows values to the right. Find t* for confidence interval and p-value for t statistic using table c with df = n 1. Note: use t value when s is unknown. Question 1: what is t distribution t(70) there is no 70. Question 1: what is t distribution t(16)

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Related Questions

6. As the test statistic becomes larger, the p-value

(a) gets smaller

(b) becomes larger 

(c) stays the same, since the sample size has not been changed

(d) becomes negative.

 

7. To describe the sampling distribution of the sample proportion, we use

(a) The sample proportion 

(b) The population proportion 

(c) The population mean

(d) The population mean

 

8. When small samples are used to estimate a population mean, in cases where the population standard deviation is unknown and the original distribution is normal:

(a) There always will be a large amount of sampling error.

(b) the t-distribution must be used to obtain the critical value.

(c) the resulting margin of error for a confidence interval estimate will tend to be fairly small.

(d) the z distribution must be used to obtain the critical value.

 

 

Module 2 Minitab Assignment

Instructions:
Below you will find questions and a sample dataset. Please use the provided dataset to complete the tasks and to answer the questions.

As reported by the U.S. Census Bureau in Current Population Reports, the percentage of adults in each state and the District of Columbia who have completed high school is provided below.
Find the mean, median, and mode for this data set. Be aware that the mode does not always exist. 
Find the range and standard deviation of this data set.
Write a sentence interpreting the mean and standard deviation.
Write a sentence interpreting the median.
Dataset:
State Percent - Dataset
Alabama 95
Alaska 89
Arizona 95
California 84
Delaware 80
Georgia 81
Illinois 88
Kansas 83
Louisiana 85
Massachusetts 85
New Mexico 91
New York 93
North Carolina 88
Oklahoma 85
Texas 88
Utah 91
Vermont 86
Washington 80
Wisconsin 81
Wyoming 95


(continued on next page) 
Based on the following data,
Determine and interpret the first, second, and third quartiles.
Determine and interpret the interquartile range.
Construct a box-plot and describe the shape of the distribution.
Identify any outliers, if any.
Dataset:
96
59
55
111
76
91
60
57
84
123
56
89
61
72
89
72
81
88
75
79














(continued on next page) 
This is a set of data from a sample of n = 11 items:
Produce a scatterplot of the data.
What does the plot suggest about the relationship between the variables? 
Find and interpret the correlation coefficient.
Find and interpret the coefficient of determination.
Predict the value of y when x = 65. How much faith do you have in this prediction? Explain.
Dataset:
x y
46.1 150.8
47.6 150.2
45.5 141.3
43.1 167.4
44.5 166.7
36.9 121.7
47.4 143.6
44.8 186.1
41.3 166.2
33.5 140.4
34.4 132.9