Chapter 8: Confidence Intervals – Two Populations Means

Confidence Intervals – Two Populations Means Inferences about Two Means with Unknown Population Standard Deviations Independent Samples Population Standard Deviations not Assumed Equal (Non-Pooled t-Interval) Assumptions • The samples are obtained using simple random sampling • The samples are independent • The populations from which the samples are drawn are normally distributed or the sample sizes are large ( n1  30, n2  30 ) The procedure is robust, so minor departures from normality will not adversely affect the results. If the data have outliers, the procedure should not be used. 6) – Schizophrenia and Dopamine Previous research has suggested that changes in the activity of dopamine, a neurotransmitter in the brain, may be a causative factor for schizophrenia. In the paper “Schizophrenia: Dopamine b-Hydroxylase Activity and Treatment Response”, Sternberg et al. published the results of their study in which they examined 25 schizophrenic patients who had been classified as either psychotic or not psychotic by hospital staff. The activity of dopamine was measured in each patient by using the enzyme dopamine b-hydroxylase to assess differences in dopamine activity between the two groups. The following are the data, in nanomoles per milliliter-hour per milligram (nmol/ml-h/mg). Psychotic 0.0150 0.0270 0.0222 0.0320 0.0204 0.0226 0.0275 0.0208 0.0306 0.0245 Non-psychotic 0.0104 0.0230 0.0145 0.020 0.0116 0.0180 0.0210 0.0252 0.0154 0.0105 0.0130 0.0170 0.0112 0.0200 0.0156 Assume the populations from which the samples were selected are normally distributed. a) Find the point estimate for the dopamine level of the Psychotic group. Construct a 98% confidence interval estimate for the dopamine level of the psychotic group. (Use the calculator) b) Find the point estimate for the dopamine level of the Non-Psychotic group. Construct a 98% confidence interval estimate for the dopamine level of the non-psychotic group. (Use the calculator) c) Compare results from (a) and (b). Do the data suggest that dopamine activity is higher, on average in psychotic patients. Assumptions • The samples are independently obtained using simple random sampling. • For both samples, the conditions np ≥ 5 and n(1 – p) ≥ 5 are both satisfied. For both samples, the sample size, is no more than 5% of the population size 7) Eating Out Vegetarian A Zogby International poll of 1181 US adults was conducted in March 1999, to gauge the demand for vegetarian meals in restaurants. The study was commissioned by the Vegetarian Resource Group and was published in the September/October 1999 issue of the Vegetarian Journal. In the survey, independent random samples of 747 US men and 434 US women were taken. Of those sampled, 276 men and 195 women said that they sometimes order a dish without meat, fish, or fowl when they eat out. a) Find the point estimate p1hat. Construct a 90% confidence interval for the proportion of US men who sometimes order a dish without meat, fish, or fowl. Use calculator. b) Find the point estimate p2hat. Construct a 90% confidence interval for the proportion of US women who sometimes order a dish without meat, fish, or fowl. Use calculator. c) Do the data provide sufficient evidence to conclude that, in the United States, the percentage of men who sometimes order a dish without meat, fish, or fowl is smaller than the percentage of women who do the same? Explain why or why not.