The image is an educational tool for statistical analysis. It details the process of hypothesis testing using a t-distribution.**Instructions:**Based on the hypotheses, find the following:- **Test Statistic =** ___ (Round to three decimal places.)- **Critical value(s) =** ___ (Round to three decimal places.)- **p-value =** ___ (Round to four decimal places.)**Description:**Students are prompted to shade the sampling distribution curve to show critical regions using the correct critical values. Arrows can be adjusted to t-scores accurate to one decimal place, which correspond to tick marks on the horizontal axis. The dropdown menu allows shading selection to the left, right, or between values.**Graph Details:**- A bell-shaped curve represents a normal distribution with a mean centered around 0.- The x-axis ranges approximately from -4 to 4.- Blue shading shows area under the curve to the left of a t-score at -1.5.**Dropdown Menu Options:**- Left of a value- Right of a value- Between two values- 2 regions**Decision Section:**- **Decision:** (Select an answer from the dropdown)**Conclusion Section:**- **Conclusion:** (Select an answer to state the claim about mean differences in miles per gallon between city and other driving conditions) **Is there a difference between the ages of Actors and Actresses?**The table shows the ages of Actors and Actresses when they received their first Oscar. Assume that the two samples are randomly selected. At the 0.1 significance level, test the claim that there is a mean difference in the ages of Actors and Actresses. *(Be sure to subtract in the same direction).*| Actor (years) | Actress (years) | Difference (years) ||---------------|-----------------|--------------------|| 60 | 60 | || 52 | 56 | || 61 | 61 | || 62 | 58 | || 36 | 36 | || 49 | 51 | || 45 | 50 | |**What are the correct hypotheses? (Select the correct symbols and values.)**- \( H_0 \): [Select an answer] [ ] [Select an answer]- \( H_1 \): [Select an answer] [ ] [Select an answer]**Original Claim**: [Select an answer]**df =** [ ]

The difference between the ages of Actors and Actress when they received first Oscar is, Actor(years) Actress(years) Difference 60 60 0 52 56 -4 61 61 0 62 58 4 36 36 0 49 51 -2 45 50 -5 Let μd is defined as the mean difference between the ages of Actors and Actress when they received first Oscar. The claim of the test is that there is a mean difference in the ages of Actors and Actresses. The hypothesis is, Null hypothesis: H0:μd=0 Alternative hypothesis: H1:μd≠0 The original claim of the test is alternative hypothesis. Thus, the original claim is H1. The degrees of freedom is, df=n-1=7-1=6 Thus, the degrees of freedom is 6.The paired t test is obtained by using EXCEL. The software procedure is given below: Enter the data. Select Data > Data Analysis >t-Test: Paired Two Sample for Means > OK. Enter Variable 1 Range as Actor. Enter Variable 2 Range as Actress. Enter Hypothesized Mean Difference as 0. Mark Labels in First Row. Enter Alpha as 0.10. Click OK. The output using EXCEL is as follows: From the output, the test statistic is -0.882, the two tailed critical value is 1.943 and the p-value is 0.4118. Thus, the test statistic is -0.882, the two tailed critical value is 1.943 and the p-value is 0.4118. The shade is the 2 regions, the graph is, Decision rule: If p-value≤α, then reject the null hypothesis. Otherwise, do not reject the null hypothesis. Conclusion: The p-value (0.4118) is greater than the level of significance (0.10). Based on decision rule, fail to reject the null hypothesis. Thus, there is no sufficient evidence to support the claim that the mean difference in the ages of Actors and Actresses.

Math

Statistics

Is there a difference between the ages of Actors and Actresses? The table shows the ages of Actors and Actress when they received their first Oscar. Assume that the two samples are randomly selected. At the 0.1 significance level, test the claim that there is a mean difference in the ages of Actors and Actresses. (Be sure to subtract in the same direction).

Is there a difference between the ages of Actors and Actresses? The table shows the ages of Actors and Actress when they received their first Oscar. Assume that the two samples are randomly selected. At the 0.1 significance level, test the claim that there is a mean difference in the ages of Actors and Actresses. (Be sure to subtract in the same direction).

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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