Question

A. You wish to test the following claim (HaHa) at a significance level of α=0.10α=0.10. Ho:μ=57.1Ho:μ=57.1. Ha:μ<57.1Ha:μ<57.1. You believe the population is normally distributed, but you do not know the standard deviation. You obtain the following sample of data:

Column A	Column B	Column C	Column D	Column E
30.1	75.6	53.5	84.7	59.2
37.2	36.5	52.7	47.3	70.9
34.9	44.3	37.2	43.8	46.8
48.2	60.6	49.6	61.5	74.7
39.8	39.8	34.1	57.9	44.8
56.1	68.4	64.5	78.7	84.7
14.2	62	42.7	73.9	50.9
24.1	59.7	53.5	51.4	54
42.7	33.2	63.5	86.9	55.3
56.6	42.7	55.7	38.6	26

What is the test statistic for this sample? (Report answer accurate to three decimal places.)
test statistic =
What is the p-value for this sample? (Report answer accurate to four decimal places.)
p-value =

B. A well-known brokerage firm executive claimed that at least 64 % of investors are currently confident of meeting their investment goals. An XYZ Investor Optimism Survey, conducted over a two week period, found that out of 64 randomly selected people, 39 of them said they are confident of meeting their goals. Suppose you are have the following null and alternative hypotheses for a test you are running: H0:p=0.64H0:p=0.64. Ha:p≠0.64Ha:p≠0.64. Calculate the test statistic, rounded to 3 decimal places. z=

C. Based on a sample of 25 people, the sample mean GPA was 2.66 with a standard deviation of 0.07. The test statistic is: (to 2 decimals). The critical value is: (to 2 decimals)

D. You wish to test the following claim (HaHa) at a significance level of α=0.05α=0.05. Ho:μ=60.2Ho:μ=60.2. Ha:μ<60.2Ha:μ<60.2. You believe the population is normally distributed, but you do not know the standard deviation. You obtain the following sample of data:

Column A	Column B	Column C	Column D
56.6	45.9	52.9	57.3
62.7	53.9	43.9	54.6
42.6	68.5	55.2	45.5
67.3	39.7	67.3	42.6
49.9	66.1	58.8	53.9
55.9	42.2	56.3	52.9
29.6	70.7	45.5	43.9

What is the critical value for this test? (Report answer accurate to three decimal places.)
critical value =
What is the test statistic for this sample? (Report answer accurate to three decimal places.)
test statistic =

Answer 1

Answer:

A. You wish to test the following claim (HaHa) at a significance level of α=0.10α=0.10. Ho:μ=57.1Ho:μ=57.1. Ha:μ<57.1Ha:μ<57.1. You believe the population is normally distributed, but you do not know the standard deviation. You obtain the following sample of data:

Column A	Column B	Column C	Column D	Column E
30.1	75.6	53.5	84.7	59.2
37.2	36.5	52.7	47.3	70.9
34.9	44.3	37.2	43.8	46.8
48.2	60.6	49.6	61.5	74.7
39.8	39.8	34.1	57.9	44.8
56.1	68.4	64.5	78.7	84.7
14.2	62	42.7	73.9	50.9
24.1	59.7	53.5	51.4	54
42.7	33.2	63.5	86.9	55.3
56.6	42.7	55.7	38.6	26

What is the test statistic for this sample? (Report answer accurate to three decimal places.)
test statistic = -2.164
What is the p-value for this sample? (Report answer accurate to four decimal places.)
p-value =0.0177

t Test for Hypothesis of the Mean
Data
Null Hypothesis                m=	57.1
Level of Significance	0.05
Sample Size	50
Sample Mean	52.114
Sample Standard Deviation	16.29478457
Intermediate Calculations
Standard Error of the Mean	2.3044
Degrees of Freedom	49
t Test Statistic	-2.1637
Lower-Tail Test
Lower Critical Value	-1.6766
p-Value	0.0177
Reject the null hypothesis

B. A well-known brokerage firm executive claimed that at least 64 % of investors are currently confident of meeting their investment goals. An XYZ Investor Optimism Survey, conducted over a two week period, found that out of 64 randomly selected people, 39 of them said they are confident of meeting their goals. Suppose you are have the following null and alternative hypotheses for a test you are running: H0:p=0.64H0:p=0.64. Ha:p≠0.64Ha:p≠0.64.

Calculate the test statistic, rounded to 3 decimal places. Z = -0.510

Z Test of Hypothesis for the Proportion
Data
Null Hypothesis            p =	0.64
Level of Significance	0.05
Number of Items of Interest	39
Sample Size	64
Intermediate Calculations
Sample Proportion	0.609375
Standard Error	0.0600
Z Test Statistic	-0.5104
Two-Tail Test
Lower Critical Value	-1.9600
Upper Critical Value	1.9600
p-Value	0.6098
Do not reject the null hypothesis

C. Based on a sample of 25 people, the sample mean GPA was 2.66 with a standard deviation of 0.07. The test statistic is: (to 2 decimals). The critical value is: (to 2 decimals)

Critical value at 0.05 level =2.06

Critical value at 0.01 level =2.80

D. You wish to test the following claim (HaHa) at a significance level of α=0.05α=0.05. Ho:μ=60.2Ho:μ=60.2. Ha:μ<60.2Ha:μ<60.2. You believe the population is normally distributed, but you do not know the standard deviation. You obtain the following sample of data:

Column A	Column B	Column C	Column D
56.6	45.9	52.9	57.3
62.7	53.9	43.9	54.6
42.6	68.5	55.2	45.5
67.3	39.7	67.3	42.6
49.9	66.1	58.8	53.9
55.9	42.2	56.3	52.9
29.6	70.7	45.5	43.9

What is the critical value for this test? (Report answer accurate to three decimal places.)
critical value =-1.703
What is the test statistic for this sample? (Report answer accurate to three decimal places.)
test statistic =-3.832

t Test for Hypothesis of the Mean
Data
Null Hypothesis                m=	60.2
Level of Significance	0.05
Sample Size	28
Sample Mean	52.93571429
Sample Standard Deviation	10.03158768
Intermediate Calculations
Standard Error of the Mean	1.8958
Degrees of Freedom	27
t Test Statistic	-3.8318
Lower-Tail Test
Lower Critical Value	-1.7033
p-Value	0.0003
Reject the null hypothesis