1. A confidence interval for the difference between the means of two normally distributed populations based on the following dependent samples is desired:Before After6 812 148 910 136 7The mean of the differences in the two sample means is found to be -1.8 ; and the standard deviation of the differences in means is found to be 0.8367. Use this information to find the 90 % confidence interval.2. A researcher intends to estimate the effect of a drug on the scores of human subjects performing a task of psychomotor coordination. The members of a random sample of 9 subjects were given the drug prior to testing, the mean score in this group was 9.78. A random sample of 10 subjects was used as a control group and given a placebo prior to testing. The mean score in this control group was 15.10. From past studies the population variance of subject prior to testing was 17.64 and the population variance of the control group was 27.01. These are considered independent samples. Assuming that the population distributions are normal, find a 95% confidence interval for the difference between the population mean scores.3. Supermarket shoppers were observed and questioned immediately after putting an item in their cart. Of a random sample of 510 choosing a product at the regular price, 320 claimed to check the price before putting the item in their cart. Of an independent random sample of 332 choosing a product at a special price, 200 made this claim. Find a 90% confidence interval for the difference between the two population proportions.4. A manufacturer of detergent claims that the contents of boxes sold weigh on average 16 ounces. The distribution of weight is known to be normal, with a standard deviation of 0.4 ounce. A random sample of 16 boxes yielded a sample mean weight of 15.84 ounces. Test at the 10% significance level the null hypothesis that the population mean weight is less than 16 ounces.
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