Statistics students believe that the mean score on a first statistics test is 65. The instructor thinks that themean score is higher. She samples 10 statistics students and obtains the scores:Grades64.385.563.99666.573.569696966.5Test grades are believed to be normally distributed.Use a significance level of 5%.A. State the alternative hypothesis: HA:Ou< 65Ομ > 65Ομ4 65B. State the mean of the sample: 72.32of (Round to two decimal places.)C. State the standard error of the sample means: 3.2861o (Round to fourdecimal places.)D. State the test statistic: t =2.2277x (Round to four decimal places.)E. State the p-value: 0.0265o (Round to four decimal places.)F. Decision:O Do not reject the null hypothesis.O Reject the null hypothesis.MChpCe24

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Description: Statistics students believe that the mean score on a first statistics test is 65. The instructor thinks that themean score is higher. She samples 10 statistics students and obtains the scores:Grades64.385.563.99666.573.569696966.5Test grades are bel

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Statistics students believe that the mean score on a first statistics test is 65. The instructor thinks that the
mean score is higher. She samples 10 statistics students and obtains the scores:
Grades
64.3
85.5
63.9
96
66.5
73.5
69
69
69
66.5
Test grades are believed to be normally distributed.
Use a significance level of 5%.
A. State the alternative hypothesis: HA:
Ou< 65
Ομ > 65
Ομ4 65
B. State the mean of the sample: 72.32
of (Round to two decimal places.)
C. State the standard error of the sample means: 3.2861
o (Round to four
decimal places.)
D. State the test statistic: t =
2.2277
x (Round to four decimal places.)
E. State the p-value: 0.0265
o (Round to four decimal places.)
F. Decision:
O Do not reject the null hypothesis.
O Reject the null hypothesis.
M
Chp
Ce
24

Expert Solution

Step 1

Solution:

Given information:

n= 10 Sample size

$μ = 65$ Population mean

let x= Grades

x	$(x - x)$	${(x - x)}^{2}$
64.3	-8.02	64.3204
85.5	13.18	173.7124
63.9	-8.42	70.8964
96	23.68	560.7424
66.5	-5.82	33.8724
73.5	1.18	1.3924
69	-3.32	11.0224
69	-3.32	11.0224
69	-3.32	11.0224
66.5	-5.82	33.8724

$\sum_{} x = 723.2 \sum_{} {(x - x)}^{2} = 971.876$

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