Final Exam - Intro to Statistics Tuesday 5/25/2021 Start 6:35 PM

  • Due May 25, 2021 at 8:30pm
  • Points 15
  • Questions 30
  • Available May 25, 2021 at 6:35pm - May 25, 2021 at 8:30pm 1 hour and 55 minutes
  • Time Limit 115 Minutes
  • Allowed Attempts 2

Instructions

LaTeX: T=\frac{sample\:mean\:-\:population\:mean}{estimated\:standard\:error}=\frac{x-\mu}{\frac{s}{\sqrt{n}}}

estimated standard error is \frac{s}{\sqrt{n}}

here is the formula for the T-statistic: = x1-bar minus x2-bar minus the quantity mu1 minus mu 2, over the square root of the sum of s1 squared over n1 and s2 squared over n2

 

x\pm margin\:of\:error=x\pm\left(critical\:value\right)\cdot\left(SE\right)

F-test Statistics = F equals the variation in sample means divided by the variation in each sample

Chi-Square Test Statistic = chi square = sum of the quantities 1 over expected times the square of expected minus observed

df = (r − 1)(c − 1), where r is the number of rows and c is the number of columns in the two-way table

One-sample T-interval: \bar{x}\pm T_c\cdot\frac{s}{\sqrt{n}}x ¯ ± T c ⋅ s n, where s is the sample standard deviation.

Confidence Interval= \left(\bar{x}_1-\bar{x}_2\right)\pm T_c\cdot\sqrt{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2}}

Convert a sample mean Xbar into a z-score: Z=\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt{n}}}

Here are the critical Z-values for commonly used confidence levels.

Confidence Level Critical Value Zc
90% 1.645
95% 1.960
99% 2.576

To estimate a difference in population proportions (or a treatment effect), the statistic is a difference in sample proportions. So the confidence interval is

(difference in sample proportions) ± margin of error

 

Also, since we do not know the values of the population proportions, we estimate the standard error by using sample proportions in the formula for the margin of error.

Zc√ˆp1(1−ˆp1)n1+ˆp2(1−ˆp2)n2

 for population proportions using the pooled proportion.

ˆp = x1 + x2n1 + n2

With this pooled proportion, we estimate the standard error to compute the Z-test statistic 

 

 

 

Only registered, enrolled users can take graded quizzes