# Statistics Analysis

Topics: Statistical hypothesis testing, Type I and type II errors, Statistics Pages: 4 (548 words) Published: February 28, 2015
﻿Hypothesis:
Ho: P = .10 (Mr. Plex and consortium will seriously consider settlement) H1: P < .10 (Mr. Plex and consortium will rigorously defend any lawsuit by Tommy) Analysis：
For this case, we use 0.01 as the significance level. In a hypothesis test, a Type I Error occurs when the null hypothesis is rejected when it is in fact true. That means if the consortium decides to consider a settlement when greater than 10% of the patrons resented ads/commercials is true and we reject the null hypothesis when in fact null hypothesis is correct, then we will make a type I error. A Type II Error occurs if Ha is true and we accept Ho when it is false. That means if the consortium will defend any lawsuit by tommy when 10% or less does not like ads/commercials is true and we accept null hypothesis when it is false, then we will make a type II error.

Analysis work for the first survey (270 patrons)
We conducted hypothesis testing with a sample size of 270 people, 20 people agree with Tommy, and resent the commercials before the movie. P = 10% (percentage for which Mr. Plex and consortium considers to determine to settle with Tommy) P^ = 20/270 = 0.074 = 7.4% (percentage of sample of those who agree with Tommy and resented the ads) n = 270 (Patrons); P= 10% = 0.1; P^ = 0.074; q = 1- 0.1=0.9

Since：
Therefore, Z = (0.074 - .10) / (√(0.10 (1 - .10) / 270))
Z = -1.424
We use a significant level of α=. 01 for a one-tailed hypothesis: P-value = 0.0772
The result is not significant at p < .01
Since .0772 is greater than the significance level of 0.01, we accept the null hypothesis. Analysis work for the second survey (583 patrons)
P = 10% = 0.1; P^ = 37 / 583 = 0.063; n = 583 (patrons);
Z = ((0.063 – .10) / (√(.10(1 - .10) / 583) )
Z = -2.978
We use a significant level of α=. 01 for a one-tailed hypothesis: P-value = 0.001451
The result is significant at p < 0.01
For the second survey of a sample of 583 patrons with 37 agreeing with Tommy, we get...