The historical reports from two major networks showed that the mean number of commercials aired during prime time was equal for both networks last year. In order to find out whether they still air the same number of commercials on average or not, random and independent samples of 100 recent prime time airings from both networks have been considered. The first network aired a mean of 109.5 commercials during prime time with a standard deviation of 5.2. The second network aired a mean of 110.5 commercials during prime time with a standard deviation of 5.3. Since the sample sizes are quite large, assume that the population standard deviations can be estimated to be equal to the sample standard deviations, 5.2 and 5.3. At the 0.10 level of significance, is there sufficient evidence to support the claim that the mean number, $\mu_1$, of commercials aired during prime time by the first station is not equal to the mean number, $\mu_2$, of commercials aired during prime time by the second station? Perform a two-tailed test. Then complete the parts below.Carry your intermediate computations to at least three decimal places. (If necessary, consult a list of formulas.) (a) State the null hypothesis $H_0$ and the alternative hypothesis $H_1$.$ H_0 $: [ ]$ H_1 $: [ ](b) Determine the type of test statistic to use.(Choose one) [ ](c) Find the value of the test statistic. (Round to three or more decimal places.)[ ](d) Find the two critical values at the 0.10 level of significance. (Round to three or more decimal places.)[ ] and [ ]---### Diagram ExplanationThe diagram consists of boxes for inputting:- Null Hypothesis ($ H_0 $)- Alternative Hypothesis ($ H_1 $)- Test statistic type (selection box)- Test statistic value- Two critical valuesMathematical symbols and symbols for mean ($\bar{x}$), proportion ($\hat{p}$), and standard deviation ($\sigma$, $s$) are shown, alongside plus/minus symbols for calculations.An "Explanation" button is present for additional help, as well as a "Check" button to validate inputs. ### Steps for Conducting a Hypothesis Test**Objective:**Determine if the mean number of commercials aired during prime time by the first station is not equal to the mean number of commercials aired during prime time by the second station using a two-tailed test.#### Steps to Follow:1. **State Hypotheses:** - **Null Hypothesis $ H_0 $:** $ H_0 $ represents the claim that there is no difference in the mean number of commercials aired between the two stations. - **Alternative Hypothesis $ H_1 $:** $ H_1 $ indicates that the means are different.2. **Determine the Test Statistic:** - Choose the type of test statistic appropriate for the hypothesis being tested (not specified in the image, but typically a t-test or z-test).3. **Calculate the Test Statistic:** - Perform calculations to find the test statistic. It's essential to round this value to three or more decimal places for precision.4. **Find Critical Values:** - Determine the critical values at the 0.10 level of significance. These values set the threshold for deciding whether to reject $ H_0 $.5. **Decision Making:** - Based on the critical values and test statistic, decide whether the data supports the claim that there is a significant difference between the two means. - A simple choice between "Yes" or "No" can be made to conclude the test.#### Additional Notes:- Ensure all intermediate computations carry at least three decimal places.- Several statistical symbols and their functions are present on-screen to facilitate the calculations (e.g., means, standard deviations).This test helps determine whether observable differences in commercial airtime are statistically significant, thus guiding broadcasting decisions.

(a) Hypotheses: H0: μ1=μ2H1: μ1≠μ2

Answered: The historical reports from two major…

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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