Let, (8.49, 10.39, 9.76, 12.66, 10.35, 10.96, 8.25, 12.14, 7.52, 8.92) iid∼N(μ,σ2) with μ∈Ris unknown and σ2 = 9. At α= 0.01 or 1% significance level, test H0 : μ= 9 against H1 : μ̸= 9. Calculate the test statistic, p-value and then comment on the null hypothesis.
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Let, (8.49, 10.39, 9.76, 12.66, 10.35, 10.96, 8.25, 12.14, 7.52, 8.92) iid∼N(μ,σ2) with
μ∈Ris unknown and σ2 = 9. At α= 0.01 or 1% significance level, test H0 : μ= 9 against H1 : μ̸= 9. Calculate the test statistic, p-value and then comment on the null hypothesis.
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- If, in a sample of n=20 selected from a normal population, X=59and S=12, what are the critical values of t if the level of significance, α, is 0.05, the null hypothesis, H0, is μ=50, and the alternative hypothesis, H1, is μ≠50? The critical values of t areWhat are the approximate numbers of participants needed for each of the following planned studies to have 80% power, assuming equal numbers in the two groups and all using the 0.05 significance level? (Be sure to give the total number of participants needed, not just the number needed for each group.) Expected Means Study M1 M2 Expected SPooled Tails (a) 106.0 122.4 82.0 1 (b) 42.7 17.1 32.0 2 (c) 10.0 8.8 2.4 1 (d) 477.0 502.0 50.0 2 Approximate Number of Participants Needed in Each Group (Assuming Equal Sample Sizes) for 80% Power for the t Test for Independent Means, Testing Hypotheses at the 0.05 Significance Level Effect Size Small (0.20) Medium (0.50) Large (0.80) One-tailed 310 50 20 Two-tailed 393 64 26A sample of men and women who had passed their driver's test either the first time or the second time were surveyed, with the following results: Results of the driving testGender First time Second timeMen 126 211Women 135 178a) Do these data suggest that there is a relationship between gender and the passing of their driver’s test from which the present sample was drawn? Let alpha=.05
- The number of contaminating particles on a silicon waferprior to a certain rinsing process was determined for eachwafer in a sample of size 100, resulting in the followingfrequencies:Number of particles 0 1 2 3 4 5 6 7Frequency 1 2 3 12 11 15 18 10Number of particles 8 9 10 11 12 13 14Frequency 12 4 5 3 1 2 1a. What proportion of the sampled wafers had at leastone particle? At least five particles?b. What proportion of the sampled wafers had betweenfive and ten particles, inclusive? Strictly between fiveand ten particles?c. Draw a histogram using relative frequency on thevertical axis. How would you describe the shape of thehistogram?Which New Jersey universities have students with higher GPAs? A researcher compares the GPA of 20 randomly selected students from each of the following 3 schools: Seton Hall, TCNJ, and Rowan. The mean GPAs were as follows: Seton Hall = 3.12, TCNJ = 3.39, Rowan = 2.90. (These are all made up, by the way.) SSwithin = 18.39 and SSbetween = 2.24. What can the researcher conclude at alpha .05?31% of all pygmy softshell toises have stripes on their shells. A herpetologist in Cititon collects a sample of 28 pygmy softshell tortoises and finds that 8 of them have stripes on their shells. Is there enough evidence to conclude, at a significance of alpha=0.05, that the proportion of pygmy softshell tortoises in Cititon with stripes on their shells is less than 31%? What is the claim? What is the null hypothesis? What is the alternative hypothesis? What is the test statistic? What is/are the critical value(s)? Do we reject the null hypothesis? What conclusion do we draw? What is the P-value for the problem above?
- Recently, the annual number of driver deaths per 100,000 for the selected age groups was as follows: Age Number of Driver Deaths per 100,000 16–19 38 20–24 36 25–34 24 35–54 20 55–74 18 75+ 28 Use the 4 steps of hypothesis testing to see if the prediction is significant with a criteria of alpha=.05 on the following data For each age group, pick the midpoint of the interval for the X value. (For the 75+ group, use 80.)Six samples of each of four types of cereal grain grown in a certain region were analyzed to determine thiamin content, resulting in the following data (µg/g). Wheat 5.3 4.4 6.1 6.1 6.6 5.8 Barley 6.4 8.1 6.2 7.5 5.9 5.6 Maize 5.7 4.8 6.5 5.0 6.1 5.2 Oats 8.2 6.1 7.9 7.1 5.4 7.3 Does this data suggest that at least two of the grains differ with respect to true average thiamin content? Use a level ? = 0.05 test.State the appropriate hypotheses. H0: ?1 ≠ ?2 ≠ ?3 ≠ ?4 Ha: at least two ?i's are equal H0: ?1 = ?2 = ?3 = ?4 Ha: at least two ?i's are unequal H0: ?1 = ?2 = ?3 = ?4 Ha: all four ?i's are unequal H0: ?1 ≠ ?2 ≠ ?3 ≠ ?4 Ha: all four ?i's are equal Compute the test statistic value. (Round your answer to two decimal places.)f = What can be said about the P-value for the test? P-value > 0.100 0.050 < P-value < 0.100 0.010 < P-value < 0.050 0.001 < P-value < 0.010 P-value < 0.001 State the conclusion in the problem context. Reject H0.…The manufacturer of a popular soft drink claims that cans of this drink contain 12 ounces. A consumer group is suspicious of this claim and believes the amount in each can is less than 12 ounces. A random sample of 18 cans is selected and the amount in each can is measured. The results are as follows: 11.9 11.9 12.0 11.9 12.0 11.7 11.6 11.5 11.6 12.0 11.8 11.7 12.2 11.5 12.1 11.8 12.1 11.8 Find the calculated P-value using the following link: http://www.statdistributions.com/t/
- The manufacturer of a popular soft drink claims that cans of this drink contain 12 ounces. A consumer group is suspicious of this claim and believes the amount in each can is less than 12 ounces. A random sample of 18 cans is selected and the amount in each can is measured. The results are as follows: 11.9 11.9 12.0 11.9 12.0 11.7 11.6 11.5 11.6 12.0 11.8 11.7 12.2 11.5 12.1 11.8 12.1 11.8 Calculate the value of the test statistic t. Express its value to two decimal places (nearest hundredth).________Which of the following tests analyzes the difference between the means of two independent samples? 1. correlated t test 2. sign test 3. t test for independent groups 4. all of theseWhich of the following is the correct reporting format of a single sample t-test with Cohen's d effect size, according to APA style? A. t = 2.28 , p < .05 1-tail test, estimated Cohen's d = 0.25, B. t = 2.28, n = 60, estimated Cohen's d = 0.25, p < .05, 1-tail test. C. t(59) = 2.28, p < .05 1-tail test, estimated Cohen's d = 0.25. D. Cohen's d = 0.25, t = 2.28, p < .05, 1-tail test E. t = 2.28, estimated Cohen's d = 0.25, p < .05 1-tail test.