Answer part B, C, D **Educational Website Transcript: Hypothesis Testing Example**A light bulb manufacturer guarantees that the mean life of a certain type of light bulb is at least 769 hours. A random sample of 23 light bulbs has a mean life of 751 hours. Assume the population is normally distributed and the population standard deviation is 61 hours. At a significance level of α = 0.05, do you have enough evidence to reject the manufacturer’s claim? Complete parts (a) through (e).**Graphs:**- The graph shows a normal distribution curve with shaded regions labeled “Reject \( H_0 \)”. - The critical regions are on both tails of the curve (left and right), indicating this is a two-tailed test. - The middle section is labeled as “Fail to reject \( H_0 \)”, which is the non-rejection region.**(c) Identify the standardized test statistic: Use technology.**\[ z = -1.42 \](Round to two decimal places as needed.)**(d) Decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim:**- **Option A:** Fail to reject \( H_0 \). There is not sufficient evidence to reject the claim that mean bulb life is at least 769 hours.- **Option B:** Fail to reject \( H_0 \). There is sufficient evidence to reject the claim that mean bulb life is at least 769 hours.- **Option C:** Reject \( H_0 \). There is sufficient evidence to reject the claim that mean bulb life is at least 769 hours.- **Option D:** Reject \( H_0 \). There is not sufficient evidence to reject the claim that mean bulb life is at least 769 hours. *(Selected option)*The selected decision: Reject \( H_0 \). There is not sufficient evidence to reject the claim that mean bulb life is at least 769 hours.-------**Explanation:**In this context, we are testing whether the sample mean of 751 hours provides enough evidence to contradict the manufacturer's claim that the mean bulb life is at least 769 hours. Based on the calculated \( z \)-score of -1.42 and the standard significance level of 0.05, the claim cannot be rejected.**Next Steps:** Proceed with analyzing further data or review other metrics to ensure bulb longevity claim.*Temperature: ### Problem ContextA light bulb manufacturer guarantees that the mean life of a certain type of light bulb is at least 769 hours. A random sample of 23 light bulbs has a mean life of 751 hours. Assume the population is normally distributed and the population standard deviation is 61 hours. At \(\alpha = 0.05\), do you have enough evidence to reject the manufacturer's claim? Complete parts (a) through (e).### (b) Identify the Critical Value(s)- Calculated \(z_0 = -1.65\)- Use a comma to separate answers as needed. Round to two decimal places as needed.### Identify the Rejection Region(s)Choose the correct answer below:- **Option A**: A graph with a bell curve centered around 0. The rejection region is shaded on the left side with the label "Reject \(H_0\)" from the critical value to the leftmost end.- **Option B**: A graph showing a right-tailed test scenario similar to option A.- **Option C**: A graph for a two-tailed test with the rejection regions shaded on both ends.### (c) Identify the Standardized Test Statistic[This part is partially obscured in the image]- Calculated value: \([-1.43]\) (rounded to two decimal places as needed).### Explanation of GraphsThe graphs illustrate the rejection regions for hypothesis testing. Each diagram includes a bell-shaped curve:- **Option A**: Illustrates a left-tailed test where the rejection region is on the left side, suggesting rejection of \(H_0\) if the test statistic falls in this shaded region.- **Option B**: Not fully visible, possibly represents a right-tailed test.- **Option C**: Shows a two-tailed test with rejection regions on both sides, implying rejection if the test statistic falls in either extreme region.These diagrams help visualize decision rules for hypothesis testing based on critical values and test statistics.

A light bulb manufacturer guarantees that the mean life of a certain type of light bulb is at least 769 hours. A random sample of 23 light bulbs has a mean life of 751 hours. Assume the population is normally distributed and the population standard deviation is 61 hours. At a= 0.05, do you have enough evidence to reject the manufacturer's claim? Complete parts (a) through (e). Reject Ho- Reject Ho- Reject Ho Reject Hg- se (c) Identify the standardized test statistic. Use technology. see z= - 1.42 (Round to two decimal places as needed.) (d) Decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim. see O A. Fail to reject Ho. There is not sufficient evidence to reject the claim that O B. Fail to reject Ho. There is sufficient evidence to reject the claim that mean bulb life is at least 769 hours. mean bulb life is at least 769 hours. O C. Reject Ho. There is sufficient evidence to reject the claim that mean bulb life is at least 769 hours. O D. Reject Ho. There is not sufficient evidence to reject the claim that mean bulb life is at least 769 hours. Next 11:59pm search 4: 75°F 4) 11,

A light bulb manufacturer guarantees that the mean life of a certain type of light bulb is at least 769 hours. A random sample of 23 light bulbs has a mean life of 751 hours. Assume the population is normally distributed and the population standard deviation is 61 hours. At a= 0.05, do you have enough evidence to reject the manufacturer's claim? Complete parts (a) through (e). Reject Ho- Reject Ho- Reject Ho Reject Hg- se (c) Identify the standardized test statistic. Use technology. see z= - 1.42 (Round to two decimal places as needed.) (d) Decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim. see O A. Fail to reject Ho. There is not sufficient evidence to reject the claim that O B. Fail to reject Ho. There is sufficient evidence to reject the claim that mean bulb life is at least 769 hours. mean bulb life is at least 769 hours. O C. Reject Ho. There is sufficient evidence to reject the claim that mean bulb life is at least 769 hours. O D. Reject Ho. There is not sufficient evidence to reject the claim that mean bulb life is at least 769 hours. Next 11:59pm search 4: 75°F 4) 11,

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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