Question

In order to conduct a hypothesis test for the population mean, a random sample of 28 observations is drawn from a normally distributed population. The resulting sample mean and sample standard deviation are calculated as 17.9 and 1.5, respectively. (You may find it useful to reference the appropriate table: z table or t table). HO: MS 17.5 against HA: > 17.5 a-1. Calculate the value of the test statistic. (Round all intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.) Test statistic a-2. Find the p-value. p-value < 0.01 0.01 s p-value < 0.025 O 0.05 s p-value < 0.10 O 0.025 s p-value < 0.05 p-value 20.10

Answer 1

Ans ) using excel>addin>phstat>one sample test

we have

t Test for Hypothesis of the Mean
Data
Null Hypothesis                m=	17.5
Level of Significance	0.05
Sample Size	28
Sample Mean	17.9
Sample Standard Deviation	1.5
Intermediate Calculations
Standard Error of the Mean	0.2835
Degrees of Freedom	27
t Test Statistic	1.4111
Upper-Tail Test
Upper Critical Value	1.7033
p-Value	0.0848
Do not reject the null hypothesis

a1 ) the value of test stat t = 1.411

a 2 ) 0.05 < p value <0.10

a3 ) option a is true

a 4 ) we conclude that population mean is greater than 17.5

using excel>addin>phstat>one sample test

we have

t Test for Hypothesis of the Mean
Data
Null Hypothesis                m=	17.5
Level of Significance	0.01
Sample Size	28
Sample Mean	17.9
Sample Standard Deviation	1.5
Intermediate Calculations
Standard Error of the Mean	0.2835
Degrees of Freedom	27
t Test Statistic	1.4111
Two-Tail Test
Lower Critical Value	-2.7707
Upper Critical Value	2.7707
p-Value	0.1696
Do not reject the null hypothesis

b1 ) the value of test stat t = 1.411

b 2 ) p value >0.10

b 3 ) option d is true

b 4 ) we cannot conclude that population mean differ from 17.5

option d is true