6. A researcher is interested in whether people are able to identify emotions co

Question

6. A researcher is interested in whether people are able to identify emotions correctly in people from other cultures. It is known that, using a particular method of measurement, the accuracy ratings of adult North Americans in general are normally distributed with a mean (µ) of 82 (out of 100)and a standard deviation of s = 4.5. The distribution is based on ratings made of emotions expressed by members of their own culture (other North Americans). In the present study, the researcher arranges to test 81 adult North Americans rating emotions of individuals from Indonesia. The mean accuracy of these individuals was 81.5.

a. State the null hypothesis and the alternative hypothesis. (1 point)

H0

 H1

b. Calculate the SE of the distribution of sample means. (1 point)

c. Using the .05 significance level (and a two-tailed test), what is the critical z-score?  (0.5 points)

d. What is the calculated z-score? (1 point)

e. What should the researcher conclude (Reject null hypothesis or fail to reject null hypothesis)? (0.5 points)

f. Write your results in APA format (1 point).

Explanation / Answer

Solution:-

a) State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: = 82

Alternative hypothesis: 82

Note that these hypotheses constitute a two-tailed test. The null hypothesis will be rejected if the sample mean is too big or if it is too small.

Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method is a one-sample z-test.

Analyze sample data. Using sample data, we compute the standard error (SE), z statistic test statistic (z).

b) SE = s / sqrt(n)

S.E = 0.50

c)

zcritical = + 1.96

d) z = (x - ) / SE

z = - 1

where s is the standard deviation of the sample, x is the sample mean, is the hypothesized population mean, and n is the sample size.

Since we have a two-tailed test, the P-value is the probability that the z statistic less than -1.0 or greater than 1.0.

Thus, the P-value = 0.3174

Interpret results. Since the P-value (0.3174) is greater than the significance level (0.05), we cannot reject the null hypothesis

e) From the above test we can conclude that people are able to identify emotions correctly in people from other cultures.

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