Statistics Homework: Hypothesis Testing and Probability Analysis

This document provides detailed solutions to a statistics homework assignment, covering two lab exercises. The first exercise focuses on hypothesis testing related to the impact of stress on eyewitness recall ability, including calculations of t-statistics, p-values, and the interpretation of results based on a 0.01 significance level. The second exercise delves into probability concepts, specifically binomial probability, using a scenario about color blindness to calculate the probability of specific outcomes. The solutions demonstrate the application of statistical formulas, interpretation of results, and the understanding of key concepts such as null hypotheses, significance levels, and p-values.

Question 1: Option D since population means are equal.
Question 2: Option E since population mean are unequal.
Question 3: The relevant formula used is stated below.
T = (1390.03-1268.41)/((156.842/10) + (137.972/10)0.5 = 1.84
Question 4: The relevant formula for standard error is shown below.
Substituting the given values, we get standard error = 147.41
Question 5 – Using df = 9 and t =1.84, p value = 0.099
Question 6- Since p value (0.099)> level of significance (0.05), hence fail to reject Null
hypothesis and option E.
Question 7- Paired t test would be used as the samples are dependent.
Question 8 – Option C
Question 9 – Option D
Question 10- Two tail hypothesis and also df = n-1 = 10-1 = 9, significance level = 0.05. The
critical values using t table come out as c and f. hence option (i) is the answer.
Question 11- the relevant excel output is shown below.

Value of t stat = 2.30
Question12
Since t stat is greater than the critical value on the higher end, hence reject the null hypothesis.
Option D is correct.
Question 13
P =(18/96) = 0.1875 or 0.19
Question 14
Option C (Refutes the claim)
Question 15
Option F (Supports the claim)
Question 16
Z value = -2.82
The relevant formula used is as follows.

Question 17
Using the z table, the p value for left tail test based on z = -2.82 comes out as 0.0024 or option B
Question 18
Option B since p value (0.0024)< level of significance (0.05), hence rejecting null hypothesis
and supporting the claim.