According to a theory in psychology, young female adults show more emotional empathy toward others than do males. A study tested this theory by examining the attitudes of a sample of 36 female college students. Each student completed the Ethic of Care Interview, which consisted of a series of statements on empathy attitudes. For the statement on emotional empathy, the sample mean response was 3.31. Assume the population standard deviation for females is 0.5. Note that empathy scores ranged from 0 to 4, where 0 = "never" and 4 ="always." Suppose it is known that male college students have an average emotional empathy score of μ = 3. Complete parts a through e below. C a. Specify the null and alternative hypotheses for testing whether female college students score higher than 3.0 on the emotional empathy scale. Ho: ▼ H₂: (Type integers or decimals. Do not round.) b. Compute the test statistic. Z= (Round to two decimal places as needed.). c. Find the observed significance level (p-value) of the test. p-value= (Round to three decimal places as needed.) d. At a = 0.01, what is the appropriate conclusion? Ho. There is (Type an integer or a decimal. Do not round.) evidence to conclude that the true mean empathy score for female college students is
According to a theory in psychology, young female adults show more emotional empathy toward others than do males. A study tested this theory by examining the attitudes of a sample of 36 female college students. Each student completed the Ethic of Care Interview, which consisted of a series of statements on empathy attitudes. For the statement on emotional empathy, the sample mean response was 3.31. Assume the population standard deviation for females is 0.5. Note that empathy scores ranged from 0 to 4, where 0 = "never" and 4 ="always." Suppose it is known that male college students have an average emotional empathy score of μ = 3. Complete parts a through e below. C a. Specify the null and alternative hypotheses for testing whether female college students score higher than 3.0 on the emotional empathy scale. Ho: ▼ H₂: (Type integers or decimals. Do not round.) b. Compute the test statistic. Z= (Round to two decimal places as needed.). c. Find the observed significance level (p-value) of the test. p-value= (Round to three decimal places as needed.) d. At a = 0.01, what is the appropriate conclusion? Ho. There is (Type an integer or a decimal. Do not round.) evidence to conclude that the true mean empathy score for female college students is
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Transcribed Image Text:According to a theory in psychology, young female adults show more emotional empathy toward others than do males. A study tested this theory by examining the attitudes of a sample of 36 female
college students. Each student completed the Ethic of Care Interview, which consisted of a series of statements on empathy attitudes. For the statement on emotional empathy, the sample mean
response was 3.31. Assume the population standard deviation for females is 0.5. Note that empathy scores ranged from 0 to 4, where 0 = "never" and 4 = "always." Suppose it is known that male
college students have an average emotional empathy score of µ = 3. Complete parts a through e below.
a. Specify the null and alternative hypotheses for testing whether female college students score higher than 3.0 on the emotional empathy scale.
Ho:
Ha:
(Type integers or decimals. Do not round.)
b. Compute the test statistic.
Z= (Round to two decimal places as needed.)
c. Find the observed significance level (p-value) of the test.
p-value = (Round to three decimal places as needed.)
d. At x = 0.01, what is the appropriate conclusion?
Ho. There is
(Type an integer or a decimal. Do not round.)
e. How small of an x-value can you choose and still have sufficient evidence to reject the null hypothesis?
evidence to conclude that the true mean empathy score for female college students is
A. There would still be sufficient evidence to reject the null hypothesis if a < 0.002.
B. There would still be sufficient evidence to reject the null hypothesis if a > 0.002.
C. There would still be sufficient evidence to reject the null hypothesis if a>0.01.
D. There would still be sufficient evidence to reject the null hypothesis if a <0.01.
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