Ghosts The following table summarizes results from a Pew Resea...

Name: A wildlife research group surveyed a sample of individuals about their expe
Uploaded: 2022-07-23T00:00:00.000Z
Duration: 6 min
Description: Watch the video explanation for the concept: A wildlife research group surveyed a sample of individuals about their expe

Question

Ghosts The following table summarizes results from a Pew Research Center survey in which subjects were asked whether they had seen or been in the presence of a ghost. Use a 0.01 significance level to test the claim that gender is independent of response. Does the conclusion change if the significance level is changed to 0.05?

Survey table: Ghost sightings by gender. Males: Yes 138, No 724. Females: Yes 228, No 913.

Accepted Answer

A wildlife research group surveyed a sample of individuals about their experiences with bird watching. Participants were asked whether they had seen a rare bird in the wild. Results are shown in the table below. We're given a table of responses from male to female, and yes and no. Test the claim that gender is independent of having seen a rare bird using a 0.01 significance level. Does the conclusion change if the significance level is instead 0.05? Let's go ahead and take a look. We're gonna have our hypotheses. This will be a chi square test. And Our no hypothesis is that. Gender And seeing A Rear bird Are Independent Where the alternative is that they are not independent of each other. And so to solve this, let's first find our expected values in our totals. So I'll make an expected table, with male or female, yes and no. We have our totals. And our male total, 32 + 48, gives us 80. Female total, 44 + 36, gives us 80. Our yes total, 32 + 44, gives us 76. No total gives us 84, and our overall grand total is 160. Now, we will find expected values for every one of these columns. Our expected value Will be a row total. Multiplied by column total. Divided by the grand total. So, for example, Male and yes, will be a row total for meals, which is 80. Multiplied by our column total for yes, 76, divided by 160. This would give us 38. We'll do the same for the other columns, male and no gives us 42. Female, yes, gives us 38. And female no gives us 42. We now have our expected table. We can now find our chi squared statistic. I 2 equals the sum of our reserved values minus our expected, squared, divided by our expected. In this case, We have our male yes square, which will be 32 minus 38 squared. Divided by expected 38. Plus male no we can say. 48 minus 42. Squared Divided by 42. Plus 44 minus 32 squad. Divided by 32 Plus 36 minus 42 squared divided by 42. We can add all these together to get the statistic being 3.609. Now we need our critical values. We first need our degrees of freedom. Degrees of freedom will be our row count minus 1 multiplied by our column count minus 1. In this case, we have 2 rows and 2 columns. This will give us 1 multiplied by 1, which gives us degrees of freedom of 1. Now we can use our chi squared table to find the critical values. We have the chi squared at 0.05 with degree of freedom of 1, and the chi squared at 0.01 with degree of freedom of 1. For the 0.051. We'll get 3.841 from the table, and from the 0.01, we'll get 6.635. Now, to reject our hypothesis, our chi squared statistic should be greater than our critical values. In this case, 3.609, is less than 3.841. 3.609 is also less than 6.635. So for both significance levels, since our value is less than the criticals, we will Fail to reject. Ar no hypothesis. We can then conclude that. Gender And seeing A rare bird Our independent At both, alpha equals 0.01. And alpha equals 0.05. And also, the conclusion does not change when having different values for alpha. That is the answer to our problem. OK, I hope to help you solve the problem. Thank you for watching. Goodbye.

Key Concepts

Chi-Square Test of Independence

Significance Level (Alpha)

Null and Alternative Hypotheses

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