# Confidence interval for a single mean using z 8

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Confidence interval for a single mean, using Z 8. Suppose that the following data appeared on a computer printout: School Mean 2 type n Exam Country State 64 99.7 96.9 Country Private 25 102.2 144.0 City State 81 104.8 238.1 City Private 16 105.0 97.6 Assume that the samples were drawn randomly from the identifiable populations. Calculate 95% confidence intervals for each of the population means and state in words what such an interval tells you. 9. A psychologist is interested in the long-term effects of divorce on children. A sample is obtained of 10 children whose parents were divorced at least 5 years before. Each child is given a personality questionnaire that measures depression. Their scores were: 83 81 75 92 84 107 63 112 Assuming that = 12, estimate the population mean: (a) using a point estimate (b) using an interval estimate that provides 90% confidence. Hypothesis test for single mean, using Z 10. A local factory has a machine which is designed to fill lemonade bottles with 600mls of liquid, with a standard deviation of 10mls. To check whether the machine is calibrated correctly, a quality control officer took a random sample of 36 bottles and found the mean amount of liquid was actually 595 ml. Assuming a normal distribution, (a) What are the appropriate H 0 and H 1 (b) Using = .05, test the hypotheses in part (a). (c) What conclusion can be made? 11. Refer to the data for schools in Q. 8. For each sample, decide whether or not it came from a population that had a mean of 100. Set at .05 and use a two-tailed test. Compare each decision with the relevant confidence interval that you calculated previously. 9.8 12.0 15.4 9.9 92 88 ?
12. If you know that Z c = 2.33 when performing a two-tailed non-directional test, what must the level of significance be?
13. Complete the following table with the appropriate t c values to include the required percentage of the area in the middle section of the t curve: Area df t c Area df t c 10 10 20 20 80% 30 95% 30 60 60 120 120 10 10 20 20 90% 30 99% 30 60 60 120 120 14. Fill out the following table with critical values of t (both one and two-tailed) for the following degrees of freedom with = .05 and = .01. Note that is the proportion of the total area in the tail or tails.
Confidence interval for single mean, using t 15. A psychologist obtained the following scores from a sample of n = 16. Assuming random sampling, calculate the 99% confidence interval for the mean of the population from which the sample was drawn. 94 94 95 96 98 99 99 99 101 102 104 105 106 106 (these are the same data from Ex. 2, Week 4) Why is the 99% confidence interval longer than the 90% interval calculated in the Week 4 tutorial? 16. A delinquency subscale of a large personality inventory has a norm of 35. researcher is interested to know whether the mean delinquency score for children from single-parent families is different to the norm. She administers the delinquency subscale to a group of 9 adolescents from single-parent homes and obtains the following scores. 101 101 A
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