Activity 1.2: Check On Directions: Check whether the sample in each problem is sufficiently Targe enough to use the Central Limit Theorem in normal approximation. Write SLS if it is sufficiently large sample,. if not write the condition/s that tow.neld knieti ort cpend their extra d like to 2. Pedro made o in the beel inin d found out mat 2 tuo loorlosgit1oine that 4 lsnoo of eanebive ou ute 4. A social worker reports that 5% of workers in a factory are below 21 years of age. Of the 70 employees surveyed, 10 said they are below 21 years old. on steoibni 5. It is believed that in the coming election, 75% of the voters in the Province of llocos Norte will vote for the administrative candidate for governor. Out of 1,170 randomly selected voters, 740 indicated that they would vote for the administrative candidate.
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- A snack food manufacturer estimates that the variance of the number of grams of carbohydrates in servings of its tortilla chips is 1.33. A dietician is asked to test this claim and finds that a random sample of 24 servings has a variance of 1.37. At α=0.01, is there enough evidence to reject the manufacturer's claim? Assume the population is normally distributed. Complete parts (a) through (e) below. (a) Write the claim mathematically and identify H0 and Ha. A. H0: σ2≤1.33 (Claim) Ha: σ2>1.33 B. H0: σ2≠1.33 Ha: σ2=1.33 (Claim) C. H0: σ2≥1.33 Ha: σ2<1.33 (Claim) D. H0: σ2=1.33 (Claim) Ha: σ2≠1.33 (b) Find the critical value(s) and identify the rejection region(s). The critical value(s) is(are) enter your response here. (Round to two decimal places as needed. Use a comma to separate answers as needed.) Choose the correct statement below and fill in the corresponding answer boxes. A. The…a hypothesis test produces a t statistic of t=2.3. if the researcher is using a two tailed test with a=0.05 how large does the sample have to bw in order to reject the null hypothesis?Question 3A comparison of two protective methods against corrosion yielded the following maximumdepth of pit(in thousand of an inch) in pieces of similar metals subjected to the respectivetreatments.Method I 68 75 69 75 70 69 72Method II 61 65 57 63 58At α = 1% use the Wilcoxon rank sum test to test the null hypothesis that the twomethods have identical medians against the alternative hypothesis that the median arenot equal.
- You wish to test the following claim (HaHa) at a significance level of α=0.10α=0.10. Ho:p1=p2Ho:p1=p2 Ha:p1>p2Ha:p1>p2You obtain 578 successes in a sample of size n1=660n1=660 from the first population. You obtain 579 successes in a sample of size n2=723n2=723 from the second population. For this test, you should NOT use the continuity correction, and you should use the normal distribution as an approximation for the binomial distribution.What is the test statistic for this sample? (Report answer accurate to three decimal places.)test statistic = What is the p-value for this sample? (Report answer accurate to four decimal places.)p-value = The p-value is... less than (or equal to) αα greater than αα This test statistic leads to a decision to... reject the null accept the null fail to reject the null As such, the final conclusion is that... There is sufficient evidence to warrant rejection of the claim that the first population proportion is greater than the…You wish to test the following claim (HaHa) at a significance level of α=0.002α=0.002. Ho:p1=p2Ho:p1=p2 Ha:p1<p2Ha:p1<p2You obtain 182 successes in a sample of size n1=431n1=431 from the first population. You obtain 182 successes in a sample of size n2=345n2=345 from the second population. For this test, you should NOT use the continuity correction, and you should use the normal distribution as an approximation for the binomial distribution.What is the test statistic for this sample? (Report answer accurate to three decimal places.)test statistic = What is the p-value for this sample? (Report answer accurate to four decimal places.)p-value = The p-value is... less than (or equal to) αα greater than αα This test statistic leads to a decision to... reject the null accept the null fail to reject the null As such, the final conclusion is that... There is sufficient evidence to warrant rejection of the claim that the first population proportion is less than the…1. Suppose that X1, Xn is an iid random sample from a distribution with pdf f(x; sigma) = 1/2 * (sigma) * e ^ (- |x| / sigma) - infinity0 0(a) Find the method of moments estimator (MME) of \sigma. Hint: See the example in lecture notes. (b) Find the maximum likelihood estimator (MLE) of \sigma. Hint: See the example in lecture notes. (c) Use central limit theorem to find the large - sample asymptotic distribution of the MLE in part (b). (d) Suppose 10 independent observations were taken from the given distribution: (0.5, 0.8, 2.2, 1.6, 2.0, 2.8, 1.5, 0.9, 2.5, 1.8). What is the numerical value of the MLE? What is the numerical value of the estimated standard deviation (standard error) of the MLE?
- You wish to test the following claim (HaHa) at a significance level of α=0.10α=0.10. Ho:p1=p2Ho:p1=p2 Ha:p1≠p2Ha:p1≠p2You obtain 82 successes in a sample of size n1=309n1=309 from the first population. You obtain 107 successes in a sample of size n2=326n2=326 from the second population. For this test, you should NOT use the continuity correction, and you should use the normal distribution as an approximation for the binomial distribution.What is the test statistic for this sample? (Report answer accurate to three decimal places.)test statistic = What is the p-value for this sample? (Report answer accurate to four decimal places.)p-value = The p-value is... less than (or equal to) αα greater than αα This test statistic leads to a decision to... reject the null accept the null fail to reject the null As such, the final conclusion is that... There is sufficient evidence to warrant rejection of the claim that the first population proportion is not equal to the second…A horticulture student is interested on the antifungal properties of three plant species. Leaf extracts from each species were mixed with agar based growth medium and poured into 5 Petri dishes. The Petri dishes were streaked with fungi isolates and the area in sq mm of fungal growth was measured after seven days. Assuming the areas of growth are not normally distributed, which is the most appropriate analysis for the experiment to find difference? A. Kruskal Wallis B. Friedman C. t-test D. sign testYou wish to test the following claim (HaHa) at a significance level of α=0.05α=0.05. Ho:p1=p2Ho:p1=p2 Ha:p1>p2Ha:p1>p2You obtain 490 successes in a sample of size n1=579n1=579 from the first population. You obtain 450 successes in a sample of size n2=545n2=545 from the second population. For this test, you should NOT use the continuity correction, and you should use the normal distribution as an approximation for the binomial distribution.What is the test statistic for this sample? (Report answer accurate to three decimal places.)test statistic = What is the p-value for this sample? (Report answer accurate to four decimal places.)p-value =
- Which of the following are specified by the central limit theorem? a. the mean of a specific sample from the distribution of sample means b. the mean of the distribution of sample means c. the shape of the distribution of sample means d. the variability for the distribution of sample meansA population of trees has a mean leaf length of 6.2 inches. A sample of 17 of these trees in a particular neighborhood has a mean length of 3.2 inches. If SS = 144 for this sample, what is Cohen's d for this example, and what is the strength of the treatment effect, which in this case is growing in a particular neighborhood?Let X ,X , ,X 1 2 n … be a random sample of size nfrom a population with mean μ and variance σ2.(a) Show that X2 is a biased estimator for μ2.(b) Find the amount of bias in this estimator.(c) What happens to the bias as the sample size n increases?