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At a magic shop, the salesperson shows you a coin that he says will land on heads more than 70% of the times it is flipped. In an attempt to convince you he's correct, the salesperson asks you to try the coin yourself. You flip the coin 65 times. (Consider this a random sample of coin flips.) The coin lands on heads 49 of those times. Complete the parts below to perform a hypothesis test to see if there is enough evidence, at the 0.10 level of significance, to support the salesperson's claim that the proportion, p, of all times the coin lands on heads is more than 70%.

At a magic shop, the salesperson shows you a coin that he says will land on heads more than 70% of the times it is flipped. In an attempt to convince you he's correct, the salesperson asks you to try the coin yourself. You flip the coin 65 times. (Consider this a random sample of coin flips.) The coin lands on heads 49 of those times. Complete the parts below to perform a hypothesis test to see if there is enough evidence, at the 0.10 level of significance, to support the salesperson's claim that the proportion, p, of all times the coin lands on heads is more than 70%.

MATLAB: An Introduction with Applications
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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### Coin Flipping Hypothesis Test At a magic shop, the salesperson shows you a coin that he claims will land on heads more than 70% of the time it is flipped. To verify this claim, the salesperson invites you to try the coin yourself. After flipping the coin 65 times, it lands on heads 49 times. We will perform a hypothesis test to check whether there is enough evidence at the 0.10 significance level to support the salesperson's claim that the proportion \( p \) of times the coin lands on heads is more than 70%. #### Steps to Perform the Hypothesis Test: **(a) State the Hypotheses:** - **Null Hypothesis (\( H_0 \))**: \( p \leq 0.70 \) - **Alternative Hypothesis (\( H_1 \))**: \( p > 0.70 \) The diagram provides an interactive tool to select these hypotheses, where each option box allows selection of the appropriate mathematical symbol and value to formulate \( H_0 \) and \( H_1 \). **(b) Z-Test Conditions:** For your hypothesis test, you will use a Z-test. To ensure that a Z-test can be conducted, verify the values: - \( np \) - \( n(1-p) \) Ensure that both values are greater than or equal to 10 under the assumption that the null hypothesis is true. Here, \( n \) is the sample size and \( p \) is the population proportion you are testing. --- **Note:** This explanation and test conditions are critical for understanding when and how to use a Z-test in hypothesis testing, especially regarding proportions in statistics.
Transcribed Image Text:### Coin Flipping Hypothesis Test At a magic shop, the salesperson shows you a coin that he claims will land on heads more than 70% of the time it is flipped. To verify this claim, the salesperson invites you to try the coin yourself. After flipping the coin 65 times, it lands on heads 49 times. We will perform a hypothesis test to check whether there is enough evidence at the 0.10 significance level to support the salesperson's claim that the proportion \( p \) of times the coin lands on heads is more than 70%. #### Steps to Perform the Hypothesis Test: **(a) State the Hypotheses:** - **Null Hypothesis (\( H_0 \))**: \( p \leq 0.70 \) - **Alternative Hypothesis (\( H_1 \))**: \( p > 0.70 \) The diagram provides an interactive tool to select these hypotheses, where each option box allows selection of the appropriate mathematical symbol and value to formulate \( H_0 \) and \( H_1 \). **(b) Z-Test Conditions:** For your hypothesis test, you will use a Z-test. To ensure that a Z-test can be conducted, verify the values: - \( np \) - \( n(1-p) \) Ensure that both values are greater than or equal to 10 under the assumption that the null hypothesis is true. Here, \( n \) is the sample size and \( p \) is the population proportion you are testing. --- **Note:** This explanation and test conditions are critical for understanding when and how to use a Z-test in hypothesis testing, especially regarding proportions in statistics.
(d) Based on your answer to part (c), choose what can be concluded, at the 0.10 level of significance, about the claim made by the salesperson. - Since the p-value is less than (or equal to) the level of significance, the null hypothesis is rejected. So, there is enough evidence to support the claim that the coin lands on heads more than 70% of the times it is flipped. - Since the p-value is less than (or equal to) the level of significance, the null hypothesis is not rejected. So, there is not enough evidence to support the claim that the coin lands on heads more than 70% of the times it is flipped. - Since the p-value is greater than the level of significance, the null hypothesis is rejected. So, there is enough evidence to support the claim that the coin lands on heads more than 70% of the times it is flipped. - Since the p-value is greater than the level of significance, the null hypothesis is not rejected. So, there is not enough evidence to support the claim that the coin lands on heads more than 70% of the times it is flipped. The image contains a graph of a symmetric probability distribution curve with numerical labels on the x-axis ranging from -3 to 3.
Transcribed Image Text:(d) Based on your answer to part (c), choose what can be concluded, at the 0.10 level of significance, about the claim made by the salesperson. - Since the p-value is less than (or equal to) the level of significance, the null hypothesis is rejected. So, there is enough evidence to support the claim that the coin lands on heads more than 70% of the times it is flipped. - Since the p-value is less than (or equal to) the level of significance, the null hypothesis is not rejected. So, there is not enough evidence to support the claim that the coin lands on heads more than 70% of the times it is flipped. - Since the p-value is greater than the level of significance, the null hypothesis is rejected. So, there is enough evidence to support the claim that the coin lands on heads more than 70% of the times it is flipped. - Since the p-value is greater than the level of significance, the null hypothesis is not rejected. So, there is not enough evidence to support the claim that the coin lands on heads more than 70% of the times it is flipped. The image contains a graph of a symmetric probability distribution curve with numerical labels on the x-axis ranging from -3 to 3.
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