Answered: A study was conducted to determine if…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Question

A study was conducted to determine if there is a difference in average reading speed between students in grade 4 and grade 5. The null hypothesis is that the means are equal, and the alternative hypothesis is that the means are not equal. A sample of 25 grade 4 students had an average reading speed of 300 words per minute with a standard deviation of 40. A sample of 30 grade 5 students had an average reading speed of 325 words per minute with a standard deviation of 35. What is the t-score and p-value for this hypothesis test?

Expert Solution

Step 1

The t-score can be calculated using the formula:

t = (x̄1 - x̄2) - (μ1 - μ2) / (s_p * sqrt(1/n1 + 1/n2))

where x̄1 and x̄2 are the sample means (300 and 325), μ1 and μ2 are the population means (assumed equal for the null hypothesis), n1 and n2 are the sample sizes (25 and 30), and s_p is the pooled standard deviation (calculated using the formula: sqrt(((n1-1)s1^2 + (n2-1)s2^2) / (n1 + n2 - 2)) / sqrt(n1 + n2)).