Question

20. A psychologist is interested in the conditions that affect the number of dreams per month that people report in which they are alone. We will assume that based on extensive previous research, it is known that in the general population the number of such dreams per month follows a normal curve, with u = 5 and 0 = 4. The researcher wants to test the prediction that the number of such dreams will be greater among people who have recently experienced a trau- matic event. Thus, the psychologist studies 36 individuals who have recently experienced a traumatic event, having them keep a record of their dreams for a month. Their mean number of alone dreams is 8. Should you conclude that people who have recently had a traumatic experience have a significantly different number of dreams in which they are alone? (a) Carry out a Z test using the five steps of hypothesis testing (use the .05 level). (b) Make a drawing of the distributions involved. (c) Explain your answer to a person who has never had a course in statistics. (d) ADVANCED TOPIC: Figure the 95% confidence interval.
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Answer 1

(20) From the given information, size of the sample n = 36, Population mean is 4 = 5, Population standard deviation is o = 4, a = 0.05, and Sample mean is 7 = 8 Null hypothesis H: 4= 5 Alternative hypothesis H: 475 It is two tailed test, since the alternate hypothesis is of notequality type(+). Level of significance a = 0.05, then the critical values are - 2002 = -1.96, and 20.025 = 1.96. - i4 8-5 . Test statistic Zca -= 4.5 ola 4/-/36 The value of the test statistic Z = 4.5, does not lies between the critical values -20025 = -1.96, and 20.025 = 1.96. We reject the null hypothesis. P-value = 2P(Z > 4.5) = 0.0000, P-value less than the level of significance a=0.05, We reject the null hypothesis. Therefore, there is enough evidence to conclude that 44+5. (2)100(1–c)% confidence interval for population mean is (7- Zarn .x+Zanim) 95% confidence interval for population mean is (3-1968).+1.96(73)-(6.6933,9.3067) As the 95% confidence interval does not consisting of zero.

Shaded area is a/2 Shaded area is a / 2 on la u=5 r Rejection region Non-rejection region Rejection region -1.96 1.96