The confidence interval contains zero, only positive values, or only negative values, so there is or is not sufficient evidence to support the claim that blue enhances performances on a creative task. ### Effects of Color on Creativity: Statistical AnalysisResearchers conducted trials to investigate how color influences creativity. Subjects were tasked with thinking of creative uses for a brick, with the setting being either a red or blue background. Responses were evaluated by judges, and the results are summarized in the accompanying table. Higher creativity scores indicate greater creativity. The claim is that "blue enhances performance on a creative task." Assume independent simple random samples from normally distributed populations, without assuming equal population standard deviations. Complete parts (a) and (b).---#### Hypothesis Testing**Objective:** Use a 0.01 significance level to test the hypothesis that a blue background enhances creative performance.**What are the null and alternative hypotheses?**- **Option A:** - \( H_0: \mu_1 \geq \mu_2 \) - \( H_1: \mu_1 < \mu_2 \)- **Option B:** - \( H_0: \mu_1 \neq \mu_2 \) - \( H_1: \mu_1 < \mu_2 \)- **Option C:** - \( H_0: \mu_1 = \mu_2 \) - \( H_1: \mu_1 > \mu_2 \)- **Option D:** - \( H_0: \mu_1 = \mu_2 \) - \( H_1: \mu_1 \neq \mu_2 \)---#### Response Summary Statistics| Background | \( \mu \) | \( n \) | \( \bar{x} \) | \( s \) ||------------|-----------|---------|---------------|---------|| Blue | \( \mu_1 \) | 48 | 4.47 | 0.51 || Red | \( \mu_2 \) | 39 | 3.64 | 0.93 |- **\( \mu \):** population mean - **\( n \):** sample size- **\( \bar{x} \):** sample mean- **\( s \):** sample standard deviation---By analyzing these statistics, you can determine whether the blue background statistically significantly enhances creativity. ### Transcription for Educational Website**Test Statistics and Conclusions**1. **Test Statistic: z = ___** - (Round to two decimal places as needed.)2. **P-Value: p = ___** - (Round to three decimal places as needed.)3. **State the Conclusion for the Test:** - **A.** Reject the null hypothesis. There is not sufficient evidence to support the claim that blue enhances performance on a creative task. - **B.** Fail to reject the null hypothesis. There is not sufficient evidence to support the claim that blue enhances performance on a creative task. - **C.** Reject the null hypothesis. There is sufficient evidence to support the claim that blue enhances performance on a creative task. - **D.** Fail to reject the null hypothesis. There is sufficient evidence to support the claim that blue enhances performance on a creative task.4. **Construct the Confidence Interval Suitable for Testing the Claim:** - Calculate the confidence interval that results in the same conclusion as part (a). \[ \mu_1 - \mu_2 = \] - (Round to two decimal places as needed.)5. **Confidence Interval:** - What is it about the confidence interval that results in the same conclusion from part (a)? - The confidence interval contains [ ___ , ___ ], so there [ is / is not ] sufficient evidence to support the claim that blue enhances performance on a creative task. ---**Note:** When filling in the blanks, ensure to round the numbers appropriately and select the correct option based on the statistical results derived from your analysis.

Given information: n1=48n2=39x¯1=4.47x¯2=3.64s1=0.51s2=0.93Level of significance (α)=0.01 Find: Test…

Researchers conducted trials to investigate the effects of color on creativity. Subjects with a red background were asked to think of creative uses for a brick; other subjects with a blue background were given the same task. Responses were scored by a panel of judges and results from scores of creativity are given in the accompanying table. Higher scores correspond to more creativity. The researchers make the claim that "blue enhances performance on a creative task." Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Complete parts (a) and (b). Click the icon to view the summary statistics. a. Use a 0.01 significance level to test the claim that blue enhances performance on a creative task. What are the null and alternative hypotheses? OA. Ho: ₁2₂ H₁: H₁ H₂ OC. Ho: H₁ H₂ H₁: Hy > H₂ Response Summary Statistics Background Blue Red Print C Done OB. Ho: H₁ #¹₂ H₁: H₁

Researchers conducted trials to investigate the effects of color on creativity. Subjects with a red background were asked to think of creative uses for a brick; other subjects with a blue background were given the same task. Responses were scored by a panel of judges and results from scores of creativity are given in the accompanying table. Higher scores correspond to more creativity. The researchers make the claim that "blue enhances performance on a creative task." Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Complete parts (a) and (b). Click the icon to view the summary statistics. a. Use a 0.01 significance level to test the claim that blue enhances performance on a creative task. What are the null and alternative hypotheses? OA. Ho: ₁2₂ H₁: H₁ H₂ OC. Ho: H₁ H₂ H₁: Hy > H₂ Response Summary Statistics Background Blue Red Print C Done OB. Ho: H₁ #¹₂ H₁: H₁

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Similar questions

In September 2011, Gallup surveyed 1,004 American adults and asked them whether they blamed Barack Obama a great deal, a moderate amount, not much, or not at all for U.S. economic problems. The results showed that 53% of respondents blamed Barack Obama a great deal or a moderate amount. Calculate the 99% confidence interval for the proportion of all American adults who blame Barack Obama a great deal or a moderate amount for U.S. economic problems. O (0.504, 0.556) O (0.499, 0.561) O (0.489, 0.571) O The confidence interval cannot be determined from the information given.
Do the t-test and test the null hypothesis that the two means are equal at the 95% confidence interval?
A clinical trial tests a method designed to increase the probability of conceiving a girl. In the study 360 babies were born, and 324 of them were girls. Use the sample data to construct a 99% confidence interval estimate of the percentage of girls born. Based on the result, does the method appear to be effective?
Several years ago, 45% of parents who had children in grades K-12 were satisfied with the quality of education the students receive. A recent poll asked 1,025 parents who have children in grades K-12 if they were satisfied with the quality of education the students receive. Of the 1,025 surveyed, 484 indicated that they were satisfied. Construct a 99% confidence interval to assess whether this represents evidence that parents' attitudes toward the quality of education have changed.
A major company would like to assess the impact of using a professional trainer to conduct a confidence-building workshop with its salespeople. A sample of 16 workers is obtained. Half (n = 8) attend the workshop and the other half (n = 8) serve as a control group. Two weeks later, each of the participants is given a questionnaire measuring the level of self-confidence. The data are as follows: Controls Workshop M = 17.5 M = 22.7 SS = 100 SS = 124 What type of t-test would you have to conduct in this scenario? Are the data sufficient to conclude that the treatment has a significant effect? Use a two-tailed test with α = .05. State the hypothesis, find the critical region, calculate your test statistic, evaluate your hypothesis then calculate the Cohen’s d measure for this scenario. State whether this is a weak, moderate, or strong effect.
Early-childhood-development studies indicate that the more often a child is read to from birth, the earlier the child begins to read. A local parents’ group wants to test this theory and samples families with young children. They find the following results. Construct a 99% confidence interval to estimate the true difference between the proportions of children who read at an early age when they are read to frequently compared to those who were read to less often, as described in the table of results. Let Population 1 be the children who were read to frequently and Population 2 be the children who were read to less often. Round the endpoints of the interval to three decimal places, if necessary. Ages when Children Begin to Read Read to at Least Three Times per Week Read to Fewer than Three Times per Week Started Reading by age 4 60 35 Started Reading after age 4 36 51 Lower end point: Upper end point:
You are told that a random sample of 150 people from Manchester New Hampshire have been given cholesterol tests, and 60 of these people had levels over the “safe” count of 200. Using Excel, construct a 95% confidence interval for the population proportion of people in New Hampshire with cholesterol levels over 200. Note: Note that this question requires confidence interval for a proportion, the interval that is likely to capture the proportion of all population members’ that satisfy a specified property. Do you remember the formula? If not, here it is:p estimate + - z-critical value X sqrt (p estimate (1-p estimate)/n) Also note that, for population proportion, we use z-multiple not the t-multiple. So you can ask, where is the population standard deviation? You don't need it. Look at the formula.
A market research business is interested in testing the hypothesis that the proportion of students who own a car is smaller for the local university campus than for the local private college. They interviewed 240 students from the university and 250 students from the private college. The number of students who owned a car was 162 at the university and 183 at the private college. Construct a 99% confidence interval for the difference in the true proportions of students who own cars at the two campuses (rounded off to three decimals).
What does the result suggest about the mean wake time of 103.0 min before a treatment? Does the drug appear to be effective? The confidence interval include or does not include the mean wake time of 103.0 min before the treatment, so the means before and after the treatment are same or are different. This result suggests that the drug treatment has or has not an effect.
in a poll, 73% of California adults (367 out of 506 surveyed) believe that education is one of the main issues facing California. We want to construct a 90% confidence interval for the true proportion of California adults who believe that education is one of the main issues facing California.- I need help with finding a 90% confidence interval for the population proportion (I also have to round the answer to three decimal places)
Several years ago, 48% of parents with children in grades K-12 were satisfied with the quality of education the students receive. A recent poll found that 469 of 1,145 parents with children in grades K-12 were satisfied with the quality of education the students receive. Construct a 99% confidence interval to assess whether this represents evidence that parents' attitudes toward the quality of education have changed. E Click the icon to view the Confidence Interval Critical Value table. What are the null and alternative hypotheses? Ho: P V versus H, : p (Type integers or decimals. Do not round.) Find the 99% confidence interval. The lower bound is The upper bound is (Round to three decimal places as needed.) What is the correct conclusion? O A. Since the interval does not contain the proportion stated in the null hypothesis, there is sufficient evidence that parents' attitudes toward the quality of education have changed. O B. Since the interval contains the proportion stated in the…
A 95% confidence interval for the proportion of students achieving a reading achievement score that is above the standard set by the teachers for a population of third grade students is (0.43, 0.49). Which is the correct interpretation of the confidence interval? a)95% of the third grade students scores between 43% and 49% of the reading achievement score. b)We are 95% confident that 43% to 49% of elementary school students achieves reading achievement score above the standard. c)We are 95% confident the true proportion of third grade students achieves reading achievement score above the standard is between 43% to 49% d)We are 95% confident that 43% to 49% of the sample of third graders achieves reading achievement score above the standard.