**(a)**An ice cream company is interested to see if the proportion of people in this town who like chocolate ice cream is significantly different than the national average. What is the hypothesis test to be done?- \( H_0: \mu = 0.5 \) - \( H_1: \mu > 0.5 \)- \( H_0: p = 0.5 \) - \( H_1: p \ne 0.5 \)- \( H_0: p = 0.5 \) - \( H_1: p > 0.5 \)- \( H_0: \mu = 0.5 \) - \( H_1: \mu \ne 0.5 \)- \( H_0: p = 0.5 \) - \( H_1: p = 0.4 \)- \( H_0: p = 0.4 \) - \( H_1: p \ne 0.4 \)**(b)**Given this hypothesis test, what is the test statistic as well as the critical value associated with \(\alpha = 0.1\), with \(\alpha = 0.05\), and with \(\alpha = 0.02\)? (Round your answers to three decimal places. Hint: all values for this part will be negative, make sure to include the negative sign in your answers)- test statistic: [_______]- critical value for \(\alpha = 0.1\): [_______]- critical value for \(\alpha = 0.05\): [_______]- critical value for \(\alpha = 0.02\): [_______]**(c)**For which value(s) of \(\alpha\) should the company reject the null hypothesis? (Select all that apply.)- \(\alpha = 0.1\). The company can reject the null hypothesis at a 10% significance level.- \(\alpha = 0.05\). The company can reject the null hypothesis at a 5% significance level.- \(\alpha = 0.02\). The company can reject the null hypothesis at a 2% significance level.- None of the above. The company cannot reject the null hypothesis for any of these values for \(\alpha\ **Ice Cream Flavor Preferences Study**When given a choice between chocolate, vanilla, and strawberry, 50% of people nationally will choose chocolate as their favorite. In a city, 100 people are polled to determine their preferred ice cream flavor among the three options. Out of these 100 people, 40 chose chocolate, 50 chose vanilla, and 10 chose strawberry.**JMP Applet Analysis**The analysis tool used is JMP, which includes various features to illustrate the data collected.**Bar Graph**A bar graph is displayed showing the distribution of preferences:- Chocolate: 40%- Strawberry: 10%- Vanilla: 50%**Frequencies Table**The frequencies table breaks down the counts and probabilities for each flavor:- Chocolate: 40 people (0.4000 probability)- Strawberry: 10 people (0.1000 probability)- Vanilla: 50 people (0.5000 probability)**Test Probabilities Analysis**The test probabilities sections compare estimated probabilities to hypothesized probabilities under different scenarios:1. **Scenario 1:** - Hypothesized Probability: Chocolate 0.4000, Strawberry 0.1000, Vanilla 0.5000 - Z Test Statistic: 0.0000, Prob > |z|: 1.0000 (indicating no significant difference)2. **Scenario 2:** - Hypothesized Probability: Chocolate 0.5000, Strawberry 0.0833, Vanilla 0.4167 - Z Test Statistic: -2.0000, Prob > |z|: 0.0455 (indicating a significant difference at a 5% level)3. **Scenario 3:** - Hypothesized Probability: Chocolate 0.3000, Strawberry 0.11667, Vanilla 0.5833 - Z Test Statistic: 2.1822, Prob > |z|: 0.0291* (indicating a significant difference)4. **Scenario 4:** - Hypothesized Probability: Chocolate 0.6000, Strawberry 0.06667, Vanilla 0.3333 - Z Test Statistic: -4.0825, Prob > |z|: <.0001* (indicating a highly significant difference)*Note: Probabilities marked with an asterisk (*) indicate statistical significance.This

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Description: **(a)**An ice cream company is interested to see if the proportion of people in this town who like chocolate ice cream is significantly different than the national average. What is the hypothesis test to be done?- \( H_0: \mu = 0.5 \) - \( H_1: \mu

Solution: It is given that 50% of people nationally choose chocolate as their favorite ice cream…

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An ice cream company is interested to see if the proportion of people in this town who like chocolate ice cream is significantly different than the national average. What is the hypothesis test to be done? O H,i H = 0.5 HiH > 0.5 O Ho: p = 0.5 Hip # 0.5 %3D Ο H: μ-0.5 HiiH # 0.5 O Ho:p 0.5 H:p = 0.5 O Ho: p = 0.4 Hip # 0.4 O (b) Given this hypothesis test, what is the test statistic as well as the critical value associated with a = 0.1, with a = 0.05, and with a = 0.02? (Round your answers to three decimal places. Hint: all values for this part will be negative, make sure to include the negative sign in your answers) test statistic critical value for a = 0.1 critical value for a = 0.05 critical value for a = 0.02 O (c) For which value(s) of a should the company reject the null hypothesis? (Select all that apply.) O a = 0.1. The company can reject the null hypothesis at a 10% significance level. O a = 0.05. The company can reject the null hypothesis at a 5% significance level. O a = 0.02. The company can reject the null hypothesis at a 2% significance level. O None of the above. The company cannot reject the null hypothesis for any of these values for a.

An ice cream company is interested to see if the proportion of people in this town who like chocolate ice cream is significantly different than the national average. What is the hypothesis test to be done? O H,i H = 0.5 HiH > 0.5 O Ho: p = 0.5 Hip # 0.5 %3D Ο H: μ-0.5 HiiH # 0.5 O Ho:p 0.5 H:p = 0.5 O Ho: p = 0.4 Hip # 0.4 O (b) Given this hypothesis test, what is the test statistic as well as the critical value associated with a = 0.1, with a = 0.05, and with a = 0.02? (Round your answers to three decimal places. Hint: all values for this part will be negative, make sure to include the negative sign in your answers) test statistic critical value for a = 0.1 critical value for a = 0.05 critical value for a = 0.02 O (c) For which value(s) of a should the company reject the null hypothesis? (Select all that apply.) O a = 0.1. The company can reject the null hypothesis at a 10% significance level. O a = 0.05. The company can reject the null hypothesis at a 5% significance level. O a = 0.02. The company can reject the null hypothesis at a 2% significance level. O None of the above. The company cannot reject the null hypothesis for any of these values for a.

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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