The following data were collected for salinity of water from a sample of municipal sources (in parts per thousand) 0.5 0.5 0.6 0.6 0.8 0.8 0.8 0.9 1.0 1.1 1.3 (a) Find a 90% confidence interval for the average salinity in all mu- nicipal sources in the sampling area. (b) If we would like to have a CI with a margin of error ±0.3, what would be the required sample size for that?
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- The data in NutritionStudy include information on nutrition and health habits of a sample of 315 people. One of the variables is VitaminUse, indicating whether a person takes a multivitamin pill regularly or occasionally or not at all. Use technology to test whether the data provide evidence that the proportion taking a vitamin pill regularly is different from 35 % given. Clearly state the null and alternative hypotheses. : : 42 : Pi : P2 :: 0.35 : 2 :: P1 : p2 :: :: r Ho: vs Hg: ::Table 1: Summary statistics of the extra sodium content (%) in the thirty samples Min. : 0.14 1st Qu.: 1.17 Median : 2.13 Mean : 2.4813 3rd Qu.: 3.86 Max. : 5.22 SD = 1.6156 Researchers believe that the average percentage of sodium content is 3%. Test the appropriate hypotheses using a 5% level of significance. Specify the following: random variable of interest parameter of interest (Symbol for the parameter) statistic you would use to estimate parameterUnfortunately, arsenic occurs naturally in some ground water. A mean arsenic level of μ=8 parts per billion (ppb) is considered safe for agricultural use. A well in Los Banos is used to water cotton crops. This well is tested on a regular basis for arsenic. A random sample of 37 tests gave a sample mean of x=7.3 ppb arsenic. It is known that σ=1.9 ppb for this type of data. Does this information indicate that the mean level of arsenic in this well is less than 8 ppb? Use the classical approach. Use α=0.01 What is the hypotheses for this problem? A: Ho μ =7.3ppb vs HA μ < 7.3ppb B: Ho μ <7.3ppb vs HA μ ≥ 7.3ppb C: Ho μ =8.0ppb vs HA μ < 8.0ppb D: Ho μ <8.0ppb vs HA μ ≥ 8.0ppb
- The average gold content from an ore sample in 36 different locations is found to be 2.6 grams per ton. a. Find the 95% and 99% confidence intervals for the mean gold content in that area. Assume that the population variance is 0.09.The tensile strength of paper using 5% hardwood and 10% hardwood are to be compared. A random sample of 41 sheets made from 5% hardwood had an average tensile strength of 1.52 lbs. with a standard deviation of 0.33 lbs. A random sample of 61 sheets made from 10% hardwood had an average tensile strength of 1.88 lbs. with a standard deviation of 0.42 lbs. Can we conclude the average tensile strength is the same for the two types of paper? Use 5% significance and p-values. Part 1) Conduct the test using the assumption that the sample standard deviations are the same as the population standard deviations. Part 2) Conduct the test using the assumption that the population standard deviations are unknown but equal (you also must assume a normal population here). Part 3) Conduct the test with only the assumption that we have simple random samples from normal populations. May you please explain which stat test you used on your calculator and why. Thank you very much for your help!A scientist wants to establish if the Mississippi’s river height has increased using data from 1970 and 2020. Historically, it’s known that the variance of the height within any given year is 4.5ft. The sample from 1970 has 80 measurements with ?1μ1 = 30ft and the sample from 2020 has 260 measurements with ?2μ2 = 31.5ft. Find a 95% confidence interval for the average increase of height.
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