MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
expand_more
expand_more
format_list_bulleted
Related questions
Question
A researcher hypothesizes that the administration of Trintellix, a new treatment for clinical depression, will decrease the number of depressive episodes experienced per week.
| PID | Pre-treatment | Post-treatment |
| 1 | 4 | 2 |
| 2 | 3 | 2 |
| 3 | 3 | 2 |
| 4 | 2 | 1 |
| 5 | 4 | 4 |
| 6 | 4 | 1 |
What is the appropriate statistical test to use for this study?
In decimal form, express the calculated statistic. Round to the nearest hundredths.
If alpha criteria is set at 0.05, is there a treatment effect?
Transcribed Image Text:The image is a standard t-distribution table which is commonly used in statistical analysis to determine the critical t-values for hypothesis testing. Below is a transcription and detailed explanation of the table contents:
### t Table
- **cum. prob (Cumulative Probability)**
- **one-tail** (Alpha level for one-tailed tests)
- **two-tails** (Alpha level for two-tailed tests)
- **Headers for t-values:**
- \( t_{.50}, t_{.25}, t_{.20}, t_{.15}, t_{.10}, t_{.05}, t_{.025}, t_{.01}, t_{.005}, t_{.001}, t_{.0005} \)
- **Degrees of Freedom (df):** This is the leftmost column of the table.
- **t-values for each df:** Each value corresponds to a specific cumulative probability under the t-distribution curve, which varies based on the degrees of freedom.
### Explanation of Components:
- **Degrees of Freedom (df):** Represents the number of independent values or quantities which can be assigned to a statistical distribution. In this table, df ranges from 2 to 1000.
- **Confidence Levels at Bottom of Table:** Indicates the percentage of confidence (50% to 99.9%) corresponding to the two-tailed t-values. This helps in determining the confidence interval for the dataset being analyzed.
- **Highlighted Rows:** Certain rows in the table are shaded blue to signify common degrees of freedom, making it easier for users to locate frequently used values.
This table aids in statistical analysis by providing critical t-values necessary for conducting hypothesis tests and forming confidence intervals, particularly when the sample size is small or when the population standard deviation is unknown.
Expert Solution
arrow_forward
Step 1
A researcher hypothesizes that the administration of Trintellix, a new treatment for clinical depression, will decrease the number of depressive episodes experienced per week.
Here, the two samples are related.
That is, the number of depressive episodes are tested before the treatment and after the treatment.
Hence, the suitable test is paired t test.
Step by stepSolved in 2 steps with 1 images
Knowledge Booster
Similar questions
- Complete parts (a) and (b) below. Click here to view Page 1 of the table of areas under the standard normal curve. Click here to view Page 2 of the table of areas under the standard normal curve. a. The test statistic in a right-tailed test is z= 1.71. Determine the P-value and decide whether, at the 5% significance level, the data provide sufficient evidence to reject the null hypothesis in favor of the alternative hypothesis. The P-value is (Round to three decimal places as needed.) This P-value V sufficient evidence to reject the null hypothesis in favor of the alternative hypothesis because it is V the significance level. b. The test statistic in a right-tailed test is z= - 0.82. Determine the P-value and decide whether, at the 5% significance level, the data provide sufficient evidence to reject the null hypothesis in favor of the alternative hypothesis. The P-value is (Round to three decimal places as needed.) This P-value sufficient evidence to reject the null hypothesis in…arrow_forwardThe manufacturer claims that your new car gets 32 mpg on the highway. You suspect that the mpg is more for your car. The 69 trips on the highway that you took averaged 35.7 mpg and the standard deviation for these 69 trips was 12.4 mpg. What can be concluded at the αα = 0.05 level of significance? For this study, we should use Select an answer z-test for a population proportion t-test for a population mean The null and alternative hypotheses would be: H0:H0: ? p μ Select an answer ≠ = < > H1:H1: ? μ p Select an answer ≠ > = < The test statistic ? t z = (please show your answer to 3 decimal places.) The p-value = (Please show your answer to 4 decimal places.) The p-value is ? > ≤ αα Based on this, we should Select an answer reject fail to reject accept the null hypothesis. Thus, the final conclusion is that ... The data suggest that the population mean is not significantly more than 32 at αα = 0.05, so there is statistically insignificant…arrow_forwardWhat is the formula for the standard error of the normal approximation to the p distribution. P=arrow_forward
- he quantitative data set under consideration has roughly a bell-shaped distribution. Apply the empirical rule to answer the following question. A quantitative data set has mean 20 and standard deviation 1. Approximately what percentage of the observations lie between 17 and 23?arrow_forwardhas a different lifespan in water at a 0.05 level of significance. Sunscreen A Sunscreen B Sunscreen C Sunscreen D 43 66 64 49 90 80 51 74 40 57 44 83 87 74 63 43 43 31 49 84 58 57 64 68 The hypotheses for this ANOVA test would be: Ho: HA = HB = µc = HD HA: At least one mean is different. (claim) a = 0.05 Complete the ANOVA table below: (round answers to 3 decimal places) df MS F p-value Between Within The decision of the test is to: reject Ho odo not reject Họ The final conclusion is:arrow_forwardA researcher expects a treatment to produce an increase in the population mean. Assuming a normal distribution, what is the critical z-score for a one tailed test with a = .01? a. +2.33 b. ±2.89 c.+1.33 d. ±2.33arrow_forward
- Refer to the ANOVA table for this regression. Source d.f. SS MS Regression 2 578,850 289,425 Error 21 378,420 18,020 Total 23 957,270 Using Appendix F on the pictures, calculate F.05, a=0.05, F statistics, R2, and R2 adj.arrow_forwardChoose the appropriate statistical test. When computing, be sure to round each answer as indicated. A dentist wonders if depression affects ratings of tooth pain. In the general population, using a scale of 1-10 with higher values indicating more pain, the average pain rating for patients with toothaches is 6.8. A sample of 30 patients that show high levels of depression have an average pain rating of 7.1 (variance 0.8). What should the dentist determine? 1. Calculate the estimated standard error. (round to 3 decimals). [st.error] 2. What is thet-obtained? (round to 3 decimals). 3. What is the t-cv? (exact value) 4. What is your conclusion? Only type "Reject" or Retain"arrow_forwardRefer to the below table. Using an alpha = 0.05, test the claim that IQ scores are the same for children in three different blood lead level groups: low lead level, medium lead level, and high lead level). One-Way Analysis of Variance Summary Table for IQ Measurements for Children among Three Blood Lead Level Groups: Low Lead Level, Medium Lead Level, and High Lead Level. Source df SS MS F p Between-group (treatment) 2 469.1827 2677.864 2.30 0.104 Within-group (error) 118 203.6918 11745.05 Total 120arrow_forward
arrow_back_ios
arrow_forward_ios
Recommended textbooks for you
- MATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
Probability and Statistics for Engineering and th...StatisticsISBN:9781305251809Author:Jay L. DevorePublisher:Cengage Learning
Statistics for The Behavioral Sciences (MindTap C...StatisticsISBN:9781305504912Author:Frederick J Gravetter, Larry B. WallnauPublisher:Cengage Learning 
Elementary Statistics: Picturing the World (7th E...StatisticsISBN:9780134683416Author:Ron Larson, Betsy FarberPublisher:PEARSON
The Basic Practice of StatisticsStatisticsISBN:9781319042578Author:David S. Moore, William I. Notz, Michael A. FlignerPublisher:W. H. Freeman
Introduction to the Practice of StatisticsStatisticsISBN:9781319013387Author:David S. Moore, George P. McCabe, Bruce A. CraigPublisher:W. H. Freeman
MATLAB: An Introduction with Applications
Statistics
ISBN:9781119256830
Author:Amos Gilat
Publisher:John Wiley & Sons Inc
Probability and Statistics for Engineering and th...
Statistics
ISBN:9781305251809
Author:Jay L. Devore
Publisher:Cengage Learning
Statistics for The Behavioral Sciences (MindTap C...
Statistics
ISBN:9781305504912
Author:Frederick J Gravetter, Larry B. Wallnau
Publisher:Cengage Learning
Elementary Statistics: Picturing the World (7th E...
Statistics
ISBN:9780134683416
Author:Ron Larson, Betsy Farber
Publisher:PEARSON
The Basic Practice of Statistics
Statistics
ISBN:9781319042578
Author:David S. Moore, William I. Notz, Michael A. Fligner
Publisher:W. H. Freeman
Introduction to the Practice of Statistics
Statistics
ISBN:9781319013387
Author:David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:W. H. Freeman