Suppose that an independent research company was tasked with testing the validity of complaints against a pesticide manufacturing firm for under-filling their 20 lb bags of pesticide. Past experience has shown that the amount of pesticide dispensed by the machines that fill the bags follows a normal distribution with a mean of 20 lb and a standard deviation of 0.6 lb. To verify the validity of the complaints, a rescarcher randomly selected 16 of the firm's 20 lb pesticide bags and recorded the following weights. 19.69, 19.5, 18.85, 18.56, 20.23, 20.3, 20.14, 19.11, 19.65, 18.87, 19.22, 19.24, 18.82, 20.23, 20.46, 18.66 If you wish, you may download the data in your preferred format. Crunchlt! CSV Excel JMP Mac Text Minitab PC Text R SPSS TICale The mean weight of the 16 bags collected was 19.471 lb. Calculate the value of the one-sample z- statistic. Give your answer precise to three decimal places.

For a new study conducted by a fitness magazine, 280 females were randomly selected. For each, the mean daily calorie consumption was calculated for a September-February period. A second sample of 240 females was chosen independently of the first. For each of them, the mean daily calorie consumption was calculated for a March-August period. During the September-February period, participants consumed a mean of 2385.7 calories daily with a standard deviation of 210. During the March-August period, participants consumed a mean of 2414.3 calories daily with a standard deviation of 285. The population standard deviations of daily calories consumed for females in the two periods can be estimated using the sample standard deviations, as the samples that were used to compute them were quite large. Construct a 90% confidence interval for u, -u,, the difference between the mean daily calorie consumption u, of females in September-February and the mean daily calorie consumption u, of females in…

In order to plan properly for production, a firm must have adequate inventory. One factor influencing the inventory policy of a firm is the standard deviation of lead time, which is the time between when goods are ordered and when they actually arrive. A computer manufacturing firm is investigating the possibility of having parts shipped using ShipCo lines. The computer firm has obtained shipping information for a sample of 36 orders made to ShipCo by comparable computer firms. The lead times are summarized in the histogram below. Based on this histogram, estimate the standard deviation of the sample of 36 lead times. Carry your intermediate computations to at least four decimal places, and round your answer to at least one decimal place.

In a test of the effectiveness of garlic for lowering​ cholesterol, 36 subjects were treated with raw garlic. Cholesterol levels were measured before and after the treatment. The changes​ (before minus​ after) in their levels of LDL cholesterol​ (in mg/dL) have a mean of 0.7 and a standard deviation of 23.1. Use a 0.01 significance level to test the claim that with garlic​ treatment, the mean change in LDL cholesterol is greater than 0. What do the results suggest about the effectiveness of the garlic​ treatment? Assume that a simple random sample has been selected. Identify the null and alternative​ hypotheses, test​ statistic, P-value, and state the final conclusion that addresses the original claim.

An agricultural company is trying to decide which type of fertilizer to use on its crops. The company concerned with the average yield on its crops as well as the variance of their yields. In a sample of 41 different fields with using fertilizer A, the average crop yield per acre is 185 tons with a standard deviation of 35 tons. In a separate sample of 61 different fields using fertilizer B, the average crop yield is 175 tons with a standard deviation of 28 tons. When testing the hypothesis (at the 5% level of significance) that the variance of one of these yields is significantly larger than the other, what is the null and alternative hypotheses?

The town of KnowWearSpatial, U.S.A. operates a rubbish waste disposal facility that is overloaded if its 4728 households discard waste with weights having a mean that exceeds 26.54 lb/wk. For many different weeks, it is found that the samples of 4728 households have weights that are normally distributed with a mean of 26.29 lb and a standard deviation of 13.05 lb.What is the proportion of weeks in which the waste disposal facility is overloaded? P(M > 26.54) = Enter your answer as a number accurate to 4 decimal places. NOTE: Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.Is this an acceptable level, or should action be taken to correct a problem of an overloaded system? Yes, this is an acceptable level because it is unusual for the system to be overloaded. No, this is not an acceptable level because it is not unusual for the system to be overloaded.

A researcher decides to measure anxiety in group of bullies and a group of bystanders using a 23-item, 3 point anxiety scale.  Assume scores on the anxiety scales are normally distributed and the variance among the group of bullies and bystanders are the same. A group of 30 bullies scores an average of 21.5 with a sample standard deviation of 10 on the anxiety scale.  A group of 27 bystanders scored an average of 25.8 with a sample standard deviation of 8 on the anxiety scale. You do not have any presupposed assumptions whether bullies or bystanders will be more anxious so you formulate the null and alternative hypothesis based on that.