Test the null hypothesis H0:μ=3.9 against the alternative hypothesis HA:μ≠3.9, based on a random sample of 29 observations drawn from a normally distributed population with x¯=4.1 and σ=0.89 calculate the appropriate p-value.
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Test the null hypothesis H0:μ=3.9 against the alternative hypothesis HA:μ≠3.9, based on a random sample of 29 observations drawn from a
calculate the appropriate p-value.
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- A researcher investigates whether or not a new cold medication affects mental alertness. A standardized test of alertness is normally distributed with μ = 64 and σ = 8. A random sample of n = 16 students are given the new cold medication and are asked to take the standardized test of alertness. For the sample of n = 16 students, the mean score on the test M = 58. Using the 7 steps of hypothesis testing determine if the new cold medication affects mental alertness (i.e., there is a difference in mental alertness with the cold medication) using α = .05 For this problem 1. State the hypothesis in words 2. State the statistical hypothesis (H1 and Ho) 3. State the α level = 4. State the decision rule and be sure to include the critical valueIn a lake pollution study, the concentration of lead in the upper sedimentary layer of a lake bottom is measured from 25 sediment samples. The sample mean and the standard deviation of the measurements are found to be 0.38 and 0.06, respectively. Suppose Ho : u = 0.34 H1: u# 0.34 (a) State Type I and Type Il errors. (b) Conduct a hypothesis test at 0.01 level of significance by doing the seven-step classical approach. (please show all seven steps, formulas, calculations and the curve)Engineers in a bottle manufacturing facility want to see if the average width of the bottle wall is less than 0.1 cm. To test this, they randomly sample 500 bottles and measure the wall width. The sample average width is 0.099 cm. They also know from previous experience that the standard deviation in wall widths for the population is 0.01 cm. Run a hypothesis test with α = 0.05 to see if the population average wall width is less than 0.1 cm.
- The yield per tract in a certain region of farmland is known to have a populationstandard deviation of 13 bushels. Using the old seed variety, the population mean yield μwas 39 bushels. A farmer tests a new seed variety on a random sample of 36 tracts, andfinds a sample mean yield of 45.2 bushels. Is the population mean yield using the newseed variety different from 39? Use α= 0.10.a. State the null hypothesis . __________________State the alternative hypothesis.____________________b. Find the test statistic. _____ c. Find the P-value for the test. _____________A random sample of 100 measurements of the resistance of electronic components produced in a period of 1 week was taken. The sample skewness was 0.63 and the sample kurtosis was 3.85. Test the null hypothesis that the population distribution is normal.A sample of n=45n=45 data values randomly collected from a normally distributed population has standard deviation s=2.6s=2.6. We wish to test the null hypothesis H0:σ=3.1H0:σ=3.1 against the alternative hypothesis H1:σ≠3.1H1:σ≠3.1 at a significance of α=0.10α=0.10. What is the value of the test statistic? Write your answer rounded to 3 decimal places. What are the critical values? Write your answers rounded to 3 decimal places.Lower CV: Upper CV: Do we reject the null hypothesis? We fail to reject the null hypothesis. We reject the null hypothesis.
- A sample of n=30n=30 data values randomly collected from a normally distributed population has standard deviation s=1.9s=1.9. We wish to test the null hypothesis H0:σ=2.4H0:σ=2.4 against the alternative hypothesis H1:σ≠2.4H1:σ≠2.4 at a significance of α=0.05α=0.05. What is the value of the test statistic? Write your answer rounded to 3 decimal places. What are the critical values? Write your answers rounded to 3 decimal places.Lower CV: Upper CV:The NAEP considers that a national average of 283 is an acceptable performance. Using α = .05, run a two-tail t-test for one sample to test Ho: µ=283 for the 2019 scores. Report the t-obt, df, and p-values. Would you reject the null hypothesis that the 2019 scores come from a population with average 283? If this is the case, does it come from a population from larger or smaller average?A normal population has mean u (unknown) and variance 0.018. A random sample of size 20 observations has been taken and its variance is found to be 0.024. Test the null hypothesis H,: o = 0.018 against H,: o < 0.018 at 5% level of significance.