The Environmental Protection Agency (EPA) has determined that safe drinking water should contain at most 1.3 mg/liter of copper, on average. A water supply company is testing water from a new source and collects water in small bottles at each of 30 randomly selected locations. The company performs a test at the a = 0.05 level of Ho: μ = 1.3 H₁:μ> 1.3 where u is the true mean copper content of the water from the new source. Which of the following is true regarding Type I and Type II errors in this setting? A Type I error would be finding convincing evidence that the mean copper content of the water from the new source is greater than 1.3 mg/liter when it really is. A Type II error would be not finding convincing evidence that the true mean copper content of the water from the new source is greater than 1.3 mg/liter when it really is. A Type II error would be not finding convincing evidence that the true mean copper content of the water from the new source is greater than 1.3 mg/liter when it really isn't. The probability of making a Type I error would be reduced if a larger a level was chosen. The probability of making a Type II error would be increased if a larger a level was chosen.

la). The null hypothesis is that the difference in the grams of sugar between ultra-processed and processed food μ = 0 (Ho: μ = 0). Write an example alternative hypothesis for the mean (µ) difference between ultra-processed foods (up) and processed foods (μ). 1b). Next, generate 1,000 samples. Let's say that you asked students in our class to calculate the difference in the amount of sugar between their ultra-processed food and processed food at home, which had a mean (u) sugar difference of 14.75 grams of sugar. Do you have evidence to reject the null hypothesis? 1c). Let's say that your sample difference in the amount of sugar between ultra-processed food and processed food at home was 4.75 grams of sugar. Do you have evidence to reject the null hypothesis? 1d). What is a 92% confidence interval for the data? Please write it using the full confidence interval interpretation language (e.g., I am 92% confident that...). le). What percent of the data lie to the left of -14.25 grams of…

PLEASE ANSWER ALL THE PARTS OF QUESTION (THIS IS NOT A HRADED ASSIGNMENT)

Interpret a P-value: The manufacturer of a medication designed to lower blood pressure claims that the mean systolic blood pressure for people taking their medication is less than 135. To test this claim, blood pressure is measured for a sample of 500 people who are taking the medication. The P-value for testing Ho: μ = 135 versus H₁: µ< 135 is P = 0.001. a. The manufacturer concludes that because the P-value is very small, we can be fairly certain that the mean pressure is less than 135, but we cannot conclude that it is a lot smaller. Is this conclusion justified?

The National Institute of Standards and Technology (NIST) offers a wide variety of “standard reference materials” (SRMs) with accurately specified analyte concentrations. SRM 1951c is intended in part for “evaluating the accuracy of clinical procedures for the determination of total cholesterol . . . in human serum.” The certified total cholesterol is 6.244 ± 0.072 mmol/L. For the sake of this question, let’s treat 6.244 mmol/L as its “true” value (μ). We will use this standard to test a method with an intrinsic variability (for an experienced analyst) of σ = 0.131 mmol/L. 1. For what value of z does exactly 95% of the area under a Gaussian curve lie between ± z? Use this multiplier to find the range of measured cholesterol concentrations that would include 95% of the trials from the “parent population” (μ and σ) given above. 2. Calculate z for a trial in which the measured total cholesterol concentration is 6.302 mmol/L.  3. What is the probability that a trial will give a cholesterol…

Your local gas company is interested in estimating the average usage during the month of January. A random sample of 1280 households found the following results: X= 82 therms and s=28 therms. Conduct a test of hypothesis to determine if the average amount exceeds 80 therms. Use a=0.02.

2. Two kinds of bumper guards, six of each kind, were mounted on a certain make of compact car. Each car was then run into a concrete wall at 5 miles per hour and the costs of repairs (in dollars) was recorded. Summary of the data is shown below. n = 6 i = 144 si = 363.20 n =6 i = 149 si = 202.00 Test at the 0.02 level of significance whether it is reasonable to assume that the two populations sampled have equal variances.