(i) Explain the Type 1 error and Type 2 Error. Identify the null and alternate hypothesis (ii) Test the claim at 5% level of confidence coefficient.
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- A study was carried out to find out if the increase in substrate concentration has an appreciable effect on the rate of a chemical reaction. With a substrate concentration of 1.5 moles per liter, the reaction was performed 15 times, with an average rate of 7.5 micromoles per 30 minutes and a standard deviation of 1.5. With a substrate concentration of 2.0 moles per liter, 12 reactions were performed, yielding an average rate of 8.8 micromoles per 30 minutes and a sample standard deviation of 1.2. Is there any reason to believe that this increase in substrate concentration is due to an increase in the rate of reaction?reason to believe that this increase in substrate concentration causes an increase in the average reaction rate of more than 0.5 micromoles per 30 minutes? Use a significance level of 0.01 and assume that the populations are approximately normally distributed with equal variances.1. The parameter of interest is:2. The hypotheses for this test are:3. The calculated test…A particular brand of tires claims that its deluxe tire averages at least 50,000 miles before it needs to be replaced. From past studies of this tire, the population standard deviation is known to be 8,000. A survey of owners of that tire design is conducted. Of the 29 tires surveyed, the mean lifespan was 45,600 miles . Using alpha = 0.05, is the data highly consistent with the claim?Note: If you are using a Student's t-distribution for the problem, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.) I also need a graph made with 95% confidence levelA laboratory claims that the mean sodium level, μ of a healthy adult is 140 mEq per liter of blood. To test this claim, a random sample of 100 adult patients is evaluated. The mean sodium level for the sample is 139 mEq per liter of blood. It is known that the population standard deviation of adult sodium levels is 12 mEq. Can we conclude, at the 0.05 level of significance, that the population mean adult sodium level differs from that claimed by the laboratory? Perform a two-tailed test. Then fill in the table below. Carry your intermediate computations to at least three decimal places, and round your responses as specified in the table. The null hypothesis: H0: __? The alternative hypothesis: H1: __? The type of test statistic: (Choose one)Z,t,Chi square,F The value of the test statistic:(Round to at least three decimal places.) __? The p-value:(Round to at least three decimal places.) __? Can we conclude that the population mean…
- A study was conducted to see if increasing the substrate concentration has an appreciable effect on the velocity of a chemical reaction. With a substrate concentration of 1.6 moles per liter, the reaction was run 16 times, with an average velocity of 7.7 micromoles per 30 minutes and a standard deviation of 1.6. With a substrate concentration of 1.9 moles per liter, 12 runs were made, yielding an average velocity of 8.9 micromoles per 30 minutes and a sample standard deviation of 1.2. Is there any reason to believe that this increase in substrate concentration cause an increase in the mean velocity of the reaction of more than 0.5 micromole per 30 minutes? Use alpha 0.01A laboratory claims that the mean sodium level, µ, of a healthy adult is 138 mEq per liter of blood. To test claim, a random sample of 100 adult patients is evaluated. The mean sodium level for the sample is 137 mEq per liter of blood. It is known that the population standard deviation of adult sodium levels is 11 mEq. Can we conclude, at the 0.01 level of significance, that the population mean adult sodium level differs from that claimed by the laboratory? Perform a two-tailed test. Then fill in the table below. Carry your intermediate computations to at least three decimal places, and round your responses as specified in the table. The null hypothesis: H0 : _____ The alternative hypothesis: H1: ______ The type of test statistic: (choose one) _______ The value of the test statistic: ______ (round to at least three decimal places.) The p-value: _____ (round to at least three decimal places.) Can we conclude that the population mean adult sodium level differs from…A manufacturer of hard safety hats for construction workers is concerned about the mean and the variation of the forces its helmets transmits to wearers when subjected to an external force. The manufacturer has designed the helmets so that the mean force transmitted by the helmets to the workers is 800 pounds (or less) with a standard deviation to be less than 40 pounds. Tests were run on a random sample of n = 40 helmets, and the sample mean and sample standard deviation were found to be 825 pounds and 48.5 pounds, respectively. Do the data provide sufficient evidence, at the α = 0.05 level, to conclude that the population standard deviation exceeds 40 pounds? What is the test statistic?
- In a manufacturing industry, the amounts which go into raw materials (Scraps) aresupposed to be normally distributed with mean GHC 36. and standard deviation GHC0.1. Once every 30 minutes a scrap is selected from the production line, and its contentsare noted precisely. If the amount of the scrap goes below GHC 35.8. or above GHC36.2, then the scrap will be declared out of control.i) If the process is in control, meaning μ = GHC 36.00. and σ = GHC.0.1, find theprobability that a scrap will be declared out of control. ii) In the situation of (i), find the probability that the number of scraps found out ofcontrol in an 8hrs day (16 inspections) will be zero. iii) In the situation of (i), find the probability that the number of scraps found out ofcontrol in an 8hrs day (16 inspections) will be exactly one. iv) If the process shifts so that μ = GHC 37 and σ = GHC 0.4, find the probability thata scrap will be declared out of control.LOUIS VUITTON Company is trying to decide whether to open a store at Bagdat street in Istanbul. Based on their previous research, its stores will be successful in regions of this size if the mean monthly family income is above 30.000 TL. The standard deviation of monthly family income in Bagdat street region is assumed to be 2.000 TL. A random sample of 25 people was obtained, and the mean monthly income was found to be 31.000 TL. Based on this sample evidence, what should LOUIS VUITTON Company decide? Explain briefly.An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 160 engines and the mean pressure was 4.1 lbs/square inch. Assume the variance is known to be 0.64 If the valve was designed to produce a mean pressure of 4.2 lbs/square inch, is there sufficient evidence at the 0.02 level that the valve performs below the specifications? State the null and alternative hypotheses for the above scenario.