Question

1a Test the claim that the mean GPA of Orange Coast students is smaller than the mean GPA of Coastline students at the 0.10 significance level.

The null and alternative hypothesis would be:

H0:pO≥pCH0:pO≥pC
H1:pO<pCH1:pO<pC

H0:pO=pCH0:pO=pC
H1:pO≠pCH1:pO≠pC

H0:μO≤μCH0:μO≤μC
H1:μO>μCH1:μO>μC

H0:pO≤pCH0:pO≤pC
H1:pO>pCH1:pO>pC

H0:μO=μCH0:μO=μC
H1:μO≠μCH1:μO≠μC

H0:μO≥μCH0:μO≥μC
H1:μO<μCH1:μO<μC

The test is:

right-tailed

two-tailed

left-tailed

The sample consisted of 35 Orange Coast students, with a sample mean GPA of 3.35 and a standard deviation of 0.06, and 35 Coastline students, with a sample mean GPA of 3.38 and a standard deviation of 0.02.

The test statistic is:  (to 2 decimals)

The p-value is:  (to 2 decimals)

Based on this we:

• Reject the null hypothesis
• Fail to reject the null hypothesis

1b)

You are conducting a test of the claim that the row variable and the column variable are dependent in the following contingency table.

	X	Y	Z
A	41	28	13
B	35	57	17

Give all answers rounded to 3 places after the decimal point, if necessary.

(a) Enter the expected frequencies below:

	X	Y	Z
A
B

(b) What is the chi-square test-statistic for this data?
      Test Statistic: χ2=χ2=

(c) What is the critical value for this test of independence when using a significance level of αα = 0.10?
      Critical Value: χ2=χ2=  

(d) What is the correct conclusion of this hypothesis test at the 0.10 significance level?

• There is sufficient evidence to warrant rejection of the claim that the row and column variables are dependent.
• There is not sufficient evidence to support the claim that the row and column variables are dependent.
• There is not sufficient evidence to warrant rejection of the claim that the row and column variables are dependent.
• There is sufficient evidence to support the claim that the row and column variables are dependent.

Remember to give all answers rounded to 3 places after the decimal point, if necessary.

please if you can show work from ti 84 please

Answer 1

1a

The null and alternative hypothesis would be:

H0:pO≥pC
H1:pO<pC

The test is: left-tailed

using excel>addin>phstat>two variance '

we have

Separate-Variances t Test for the Difference Between Two Means
(assumes unequal population variances)
Data
Hypothesized Difference	0
Level of Significance	0.05
Population 1 Sample
Sample Size	35
Sample Mean	3.35
Sample Standard Deviation	0.06
Population 2 Sample
Sample Size	35
Sample Mean	3.38
Sample Standard Deviation	0.02
Intermediate Calculations
Numerator of Degrees of Freedom	0.0000
Denominator of Degrees of Freedom	0.0000
Total Degrees of Freedom	41.4634
Degrees of Freedom	41
Separate Variance Denominator	0.0107
Difference in Sample Means	-0.03
Separate-Variance t Test Statistic	-2.8062
Lower-Tail Test
Lower Critical Value	-1.6829
p-Value	0.0038

The test statistic is: -2.81

The p-value is: 0.00

Based on this we:

• Reject the null hypothesis

1b)

You are conducting a test of the claim that the row variable and the column variable are dependent in the following contingency table.

using excel>addin>phstat>chi square test

we have

Chi-Square Test
Observed Frequencies
	Column variable			Calculations
	X		Y	Z	Total		fo-fe
A	41		28	13	82		8.371728	-8.49215	0.120419
B	35		57	17	109		-8.37173	8.492147	-0.12042
Total	76		85	30	191
Expected Frequencies
	Column variable
	X		Y	Z	Total		(fo-fe)^2/fe
A	32.62827		36.49215	12.87958	82		2.148009	1.976221	0.001126
B	43.37173		48.50785	17.12042	109		1.615933	1.486699	0.000847
Total	76		85	30	191
	Data
	Level of Significance	0.1
	Number of Rows	2
	Number of Columns	3
	Degrees of Freedom	2
	Results
	Critical Value	4.60517
	Chi-Square Test Statistic	7.228835
	p-Value	0.026933
	Reject the null hypothesis
Reject the null hypothesis

(a) Enter the expected frequencies below:Give all answers rounded to 3 places after the decimal point, if necessary.

	Column variable
	X	Y	Z
A	32.628	36.492	12.880
B	43.372	48.508	17.120

(c) What is the critical value for this test of independence when using a significance level of αα = 0.10?(b) What is the chi-square test-statistic for this data?
      Test Statistic: χ2=7.223

      Critical Value: χ2=4.605

(d) What is the correct conclusion of this hypothesis test at the 0.10 significance level?

• There is sufficient evidence to support the claim that the row and column variables are dependent.