Homework SourseThe Empirical Rule tells us the following about the random v
The Empirical Rule tells us the following about the random variable X under the normal distribution. Select one: a. the sampling distribution of the mean will be normal provided that sample sizes are 30 or more b. the probability of the variable X falling less than one standard deviation below the mean is 0.16 c. the probability of the variable X falling less than one standard deviation below the mean is 0.05 d. the probability of the variable X falling less than one standard deviation below the mean is 0.025
Question 7 Not yet answered Points out of 4 Not flaggedFlag question Question text Lenny Fishface wants to compare the average Exam 1 grades between two classes (early and late). But first, Lenny has to decide what test he should run in Excel. Suppose, his sample data show Early Section Later Section Sample Mean 82 81 Sample Variance 294 172 Observations 29 34 Using a critical F value of 1.80 (from the 0.5% significance level), what test should Lenny run to compare the means? Select one: a. the equal variance t-test b. the unequal variance t-test c. a z test for two proportions d. a t-test for two dependent samples
Question 8 Not yet answered Points out of 4 Not flaggedFlag question Question text Professor Slackerstein suspects he is losing his touch. This semester, his class (of 100 students) scored an average of 78 on Exam 3 with a standard deviation of 5 points. Dr. Slackerstein wants to compare this semesters average grade to his historic average of 80. To do so, he uses the sample of 100 students and conducts a two-tail hypothesis test at the 0.05 level. What does he conclude? Select one: a. This semester’s grade is significantly different from the historic grade b. This semester’s grade is NOT significantly different from the historic grade c. This semester’s grade is statistically equivalent to 80 d. More information is required to conduct the test
Question 9 Not yet answered Points out of 4 Not flaggedFlag question Question text A researcher wants to determine if the proportion of people that believe climate change is happening is different between the United States and Canada. A survey was conducted, and 600 out of 1,000 Americans said they believed climate change is real. Out of 1,000 Canadians, 640 responded that they believed climate change is real. Using a two-tail test to compare the two proportions, what is the p-value? Select one: a. 0.0658 b. 0.0329 c. 0.0146 d. 0.0292
Solution
The Empirical Rule tells us the following about the random variable X under the normal distribution. Select one:
a. the sampling distribution of the mean will be normal provided that sample sizes are 30 or more
b. the probability of the variable X falling less than one standard deviation below the mean is 0.16
c. the probability of the variable X falling less than one standard deviation below the mean is 0.05
d. the probability of the variable X falling less than one standard deviation below the mean is 0.025
( 68% of data with in 1 sd of mean)
Question 7 Not yet answered Points out of 4 Not flaggedFlag question Question text Lenny Fishface wants to compare the average Exam 1 grades between two classes (early and late). But first, Lenny has to decide what test he should run in Excel. Suppose, his sample data show Early Section Later Section Sample Mean 82 81 Sample Variance 294 172 Observations 29 34 Using a critical F value of 1.80 (from the 0.5% significance level), what test should Lenny run to compare the means? Select one:
a. the equal variance t-test
b. the unequal variance t-test
c. a z test for two proportions
d. a t-test for two dependent samples
( variances are equal, F=294/172=1.71 which is < 1.80 the table value.)
Question 8 Not yet answered Points out of 4 Not flaggedFlag question Question text Professor Slackerstein suspects he is losing his touch. This semester, his class (of 100 students) scored an average of 78 on Exam 3 with a standard deviation of 5 points. Dr. Slackerstein wants to compare this semesters average grade to his historic average of 80. To do so, he uses the sample of 100 students and conducts a two-tail hypothesis test at the 0.05 level. What does he conclude? Select one:
a. This semester’s grade is significantly different from the historic grade
b. This semester’s grade is NOT significantly different from the historic grade
c. This semester’s grade is statistically equivalent to 80
d. More information is required to conduct the test
t Test for Hypothesis of the Mean
Data
Null Hypothesis m=
80
Level of Significance
0.05
Sample Size
100
Sample Mean
78
Sample Standard Deviation
5
Intermediate Calculations
Standard Error of the Mean
0.5000
Degrees of Freedom
99
t Test Statistic
-4.0000
Two-Tail Test
Lower Critical Value
-1.9842
Upper Critical Value
1.9842
p-Value
0.0001
Reject the null hypothesis
Question 9 Not yet answered Points out of 4 Not flaggedFlag question Question text A researcher wants to determine if the proportion of people that believe climate change is happening is different between the United States and Canada. A survey was conducted, and 600 out of 1,000 Americans said they believed climate change is real. Out of 1,000 Canadians, 640 responded that they believed climate change is real. Using a two-tail test to compare the two proportions,
what is the p-value? Select one:
a. 0.0658
b. 0.0329
c. 0.0146
d. 0.0292
Z Test for Differences in Two Proportions
Data
Hypothesized Difference
0
Level of Significance
0.05
Group 1
Number of Items of Interest
600
Sample Size
1000
Group 2
Number of Items of Interest
640
Sample Size
1000
Intermediate Calculations
Group 1 Proportion
0.6
Group 2 Proportion
0.64
Difference in Two Proportions
-0.04
Average Proportion
0.6200
Z Test Statistic
-1.84
Two-Tail Test
Lower Critical Value
-1.9600
Upper Critical Value
1.9600
p-Value
0.0658
Do not reject the null hypothesis
| t Test for Hypothesis of the Mean | |
| Data | |
| Null Hypothesis m= | 80 |
| Level of Significance | 0.05 |
| Sample Size | 100 |
| Sample Mean | 78 |
| Sample Standard Deviation | 5 |
| Intermediate Calculations | |
| Standard Error of the Mean | 0.5000 |
| Degrees of Freedom | 99 |
| t Test Statistic | -4.0000 |
| Two-Tail Test | |
| Lower Critical Value | -1.9842 |
| Upper Critical Value | 1.9842 |
| p-Value | 0.0001 |
| Reject the null hypothesis |
