USE EXCEL RESULTS FOR QUESTIONS #1 - #4

1.The weight loss programs wants to determine the changes for better weight loss. She selected 25 weight loss members at random and compared their weight for 6 months the excel results are below:

Person Before After

1 176 164

2 192 191

3 185 176

4 177 176

5 196 185

6 178 169

7 196 196

8 181 172

9 158 158

10 201 193

11 191 185

12 193 189

13 176 175

14 212 210

15 177 173

16 183 180

17 210 204

18 198 192

19 157 152

20 213 200

21 161 161

22 177 166

23 210 203

24 192 186

25 178 170

(the weight labeled "After" represents their weight 6 months later and "Before" represents their weight at the start of the six-month period). The director used .05 as a significance level.

Use excel to test. For each paired difference computer After-Before. In Data Analysis, t-Test: Paired Two Samples for means, select the After data for Variable 1 Rang. Note that the critical value output by Data Analysis for this test is always positive. In this problem, the sign of the critical value is negative corresponding to a 1-tailed test with lower reject region and negative lower critical value.

What are the Null and Alternate Hypothesis?

a. H0: AFTER-BEFORE 0; HA: AFTER-BEFORE < 0

b.H0: After-Before =0; HA: After-Before = 0

c.H0: After - Before 0; HA After-Before >0

d.H0: After-Before >0; HA: After-Before 0

2.Use the Excel to test. For each paired difference, computer After-Before. In data Analysis, t-test: Paired Two Sample for means, select the After data for Variable 1 Range. Note that the critical value output by Data Analysis for this test is always positive. In this problem. The sign of the critical value is negative corresponding to a 1-tailed test with lower reject region and negative lower critical value.

What is the t-statistic (t-score)

a. 7.087

b. -7.087

c. 9.321

d. -9.321

3.Use excel to test. For each paired difference, computer After-Before. In data Analysis, t-test: Paired Two Sample for means, select the After data for Variable 1 Range. Note that the critical value output by Data Analysis for this test is always positive. In this problem. The sign of the critical value is negative corresponding to a 1-tailed test with lower reject region and negative lower critical value.

What is the critical t-value

a. 3.645 or -3.645

b. 5.614 or -5.614

c. 1.711 or -1.711

d. 7.861 or -7.861

4.Use excel to test. For each paired difference, computer After-Before. In data Analysis, t-test: Paired Two Sample for means, select the After data for Variable 1 Range. Note that the critical value output by Data Analysis for this test is always positive. In this problem. The sign of the critical value is negative corresponding to a 1-tailed test with lower reject region and negative lower critical value.

What is your conclusion

a. reject the NULL hypothesis because the actual value is greater than critical value

b. reject the NULL hypothesis because the actual value is less than the critical value

c. do not reject the NULL hypothesis because the actual value is greater than the critical value

5.A new drug is created to help people with depression. When testing the drug, what are the null and alternative hypotheses?

a. H0: As a result of 300mg./day of the ABC drug, there will be no significant difference in depression. HA: As a result of 300mg/day of the ABC drug, there will be a significant difference in depression.

b.H0:As a result of 300mg/day of the ABC drug, there will be a significant difference in depression. HA: As a result of 300mg/day of the ABC drug, there will be no significant difference in depression.

6.Match the null hypothesis H₀ to the correct alternative H₁

a.H_0: Lot A tensile strength is comparable to lot B tensile strength

b.H_0: Lot A tensile strength is not greater than lot B tensile strength

c.H_0: Lot A tensile strength exceeds or equals lot B tensile strength

1: H_1: The mean of Lot A tensile strength is < the mean of Lot B tensile strength

2: H_1: The mean of Lot A tensile strength is > the mean of Lot B tensile strength

3: H_1: The mean of Lot A tensile strength = the mean of Lot B tensile strength

7.H0: Prototype design has at most 37 mpg vs HA: Prototype design has greater than 37 mpg. If H0 is rejected, this action will be move the prototype design to production. What kind of test is required?

a. Two tailed test with upper and lower reject regions

b. One tailed test with upper reject regions

c. One tailed test with lower reject regions

8.Math up the following:

1.The risk of we are willing to take of a type 1 error, or the type 1 error rate

2.The probability of a type 2 error

3.Not reject H0 when H0 is false

4.Reject H0 when H0 is true

5.The power of a test = P(rejecting H0|H0 false)

6.Reject H0 when H0 is false, or not reject H0 when H0 is not false

a. Type 1 error

b. Type 2 error

c. Not an error

d.

e.

f. 1-

9.For a test of the population proportion, what is the distribution of the test statistics?

a. T

b. F

c. Z

10.H0: 16.92 vs HA: > 16.92 . What is the test statistics for sample of size 21, mean 12.22, and standard deviation 1.04? Enter the test statistic with 2 decimal digits

11.A sample of size 20 yields a sample mean of 23.5 a sample standard deviation of 4.3. Test H0: Mean 25 at = 0.10. HA: Mean , 25. This is one-tailed test with lower reject region bounded by a negative critical value

a. None of the answers are correct

b. P value 0.135 H0 not rejected Conclude mean 25 plausible

c. P value 0.932 H0 not rejected Conclude mean 25 plausible

d. P value 0.068 H0 rejected Conclude mean < 25

12.The results of sampling independent populations:

sample 1 from population 1 sample 2 population 2

• mean 80 - mean 82
• population variance 3 - population variance 2
• sample size 25 - sample size 50

Note that the population variances are known. Test H0: (population 1 mean - population 2 mean) 0 at =0.05. HA: (population 1 mean - population 2 mean) > 0. This is a one-tailed test with upper reject region and positive critical value

a. P value 0.0062. H0 rejected. Conclude difference of means >0

b. P value 0.0124. H0 rejected. Conclude difference of means >0

c. P value 0.9938. H0 not rejected. Conclude difference of means 0 is plausible

13.The results of sampling independent populations:

sample 1 from population 1 sample 2 from population 2

-mean 1000 -mean 1250

-sample standard deviation 400 -sample standard deviation

-sample size 50 -sample size 75

Test the H0: population 1 mean = population 2 mean at =0.01. HA: population1 mean = population2 mean. This is a two-tailed test with both a negative lower critical value and a positive upper critical value. Separate variance is assumeD

a. test statistics of -3.09 < critical value of -1.29. H0 reject. conclude difference of means = 0

b. test statistics of -65.28 > critical value of -1.29. H0 rejected. conclude difference of means =0

c. test statistics of 65.28 > critical value of -2.36. H0 is not rejected. conclude difference of means = 0

d. test statistics of -3.09 < critical value of -2.62. H0 rejected. Conclude difference of means = 0