Which of the following is FALSE about a test statistic
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Which of the following is FALSE about a test statistic?
The obtained test statistic computed using our sample data can be considered a realization of a random variable.
A test statistic is a sample statistic used in hypothesis testing.
Across repeated samples, the test statistic is considered a random variable with a specific probability distribution.
During the hypothesis testing, we construct the sampling distribution of the test statistic assuming that the alternative hypothesis is true.
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- Suppose that you want to perform a hypothesis test based on independent random samples to compare the means of two populations. For each part, decide whether you would use the pooled t-test, the nonpooled t-test, the Mann– Whitney test, or none of these tests if preliminary data analyses of the samples suggest that the two distributions of the variable under consideration are a. normal but do not have the same shape.b. not normal but have the same shape.c. not normal and do not have the same shape; both sample sizes are large.A biologist wishes to study the effect of the pollinating number of insects on yields of dates on a large dates farm located in the governorate of Musandam. Using your statistics knowledge, you propose to her that for better inferential statistics she should use systematic random sampling to select a sample of 100 date trees from the 2000 date trees in the farm. Which of the following is true? Select one: O a. The population is 100 date trees selected from the farm O b. Systematic sampling is a convenient sampling method O c. The sampling size will be 20 O d. Systematic sampling is obtained by taking every pth element from the populationBill Alther is a zoologist who studies Anna's hummingbird (Calypte anna).† Suppose that in a remote part of the Grand Canyon, a random sample of six of these birds was caught, weighed, and released. The weights (in grams) were as follows. 3.7 2.9 3.8 4.2 4.8 3.1 The sample mean is x = 3.75 grams. Let x be a random variable representing weights of hummingbirds in this part of the Grand Canyon. We assume that x has a normal distribution and σ = 0.70 gram. Suppose it is known that for the population of all Anna's hummingbirds, the mean weight is μ = 4.45 grams. Do the data indicate that the mean weight of these birds in this part of the Grand Canyon is less than 4.45 grams? Use α = 0.05. How to solve for p
- A. Determine the mean or expected value of each Random Variable. 1. 3 4 12 20 P(s) 0.1 0.5 0.2 0.2 10 20 2. P(t) 50% 12% 38% 1/12 1/2 1/6 1/10 1/3 1/5 1/2 1/5 3. P(w) B. Answer the following questions in your own understanding. 1. How to compute the mean of a discrete random variable? State the 3 steps. Write your answer in your answer sheets.Students investigating the packaging of tortilla chips purchased 6 bags of chips marked with a net weight of 29.4 grams. They carefully weighed the contents of each bag, recording the following weights (in grams): 29.1, 28.1, 29.4, 28.6, 28.7, 28.8. Complete parts a through f below. a) Do these data satisfy the assumptions for inference? Explain. O A. The Randomization Condition is not met and cannot be assumed to be true. The histogram is unimodal and roughly symmetric, so the Nearly Normal Condition is met. O B. The Randomization Condition is met. The histogram is bimodal and not symmetric, so the Nearly Normal Condition is not met. O.C. The Randomization Condition is met. The histogram is extremely skewed right, so the Nearly Normal Condition is not met. D. The Randomization Condition may not be satisfied. However, it is reasonable to think that these bags are representative of all bags of chips. The histogram is unimodal and roughly symmetric, so the Nearly Normal Condition is met.…Q- You ............. .................drug?
- Bill Alther is a zoologist who studies Anna's hummingbird (Calypte anna).† Suppose that in a remote part of the Grand Canyon, a random sample of six of these birds was caught, weighed, and released. The weights (in grams) were as follows. 3.7 2.9 3.8 4.2 4.8 3.1 The sample mean is x = 3.75 grams. Let x be a random variable representing weights of hummingbirds in this part of the Grand Canyon. We assume that x has a normal distribution and ? = 0.86 gram. Suppose it is known that for the population of all Anna's hummingbirds, the mean weight is ? = 4.60 grams. Do the data indicate that the mean weight of these birds in this part of the Grand Canyon is less than 4.60 grams? Use ? = 0.10. (a) Compute the z value of the sample test statistic. (Round your answer to two decimal places.) (b) Find (or estimate) the P-value. (Round your answer to four decimal places.)Two different professors teach an introductory statistics course. The table shows the distribution of final grades they reported. We wonder whether one of these professors is an "easier" grader. Answer parts a) and b) below. Prof. Alpha Prof. Betal A 6. 11 B. 6. 14 12 Below C 11 4. 11 C.... a) Find the expected counts for each cell in this table. Prof. Alpha Prof. Beta (Round to two decimal places as needed.) A B Below C b) Test the hypothesis about the two professors, and state an appropriate conclusion. (Assume a significance level of a= 0.05) State the appropriate null and alternative hypotheses. Choose the correct answer below. O A. Ho: The grade distributions are different. HA: The grade distribution is the same for both professors. O B. Ho: The grade distribution is the same for both professors. Ha: Professor Beta gives out more C's than Professo Alpha. OC. H: The grade distribution is the same for both professors. HA: Professor Alpha gives out more A's than Professor Beta. OD.…We toss three symmetrical coins. If all the coins are heads, we win $10, if all the coins are tails, we win $5, if exactly two heads are heads, we lose $10, and if exactly two tails are heads, we lose $1. Determine the distribution of the random variable that assigns a win to the result of the toss, calculate its expected value, variance, and standard deviation.
- b. A manufacturer conducts a study to determine individuals who would like to own an iWatch. To collect the data, people are sent a survey via email. The following table summarises the data collected that relates to the peoples' gender. Male Female Total 32 ( ) 20 ( Want iWatch Don't Want iWatch 118 ( ) 120 ( Total i. Find all expected counts and add them to the table above. ii. Conduct an appropriate hypothesis test, at a 5% level of significance, to determine whether the desire to own an iWatch and the consumer's gender is not independent. )1.) Why does a large value of the F statistics provide evidence against the null hypothesis? 2.) An urn contains 20 colored golf balls: 8 white, 6 red, 4 blue, and 2 yellow. A child is allowed to draw balls until he gets a yellow one. The number of draws required is recorded. Determine what distribution the probability experiment represents and why?According to the Federal Trade Commission report on consumer fraud and identity theft, 23% of all complaints in 2007 were for identity theft. This year, a certain state kept track of the number of its 1325 complaints were for identity theft. They want to know if the data provide enough evidence to show that this state had a different proportion of identity theft than 23%? State the random variable, population parameter, and hypotheses. Fill in the correct null and alternative hypotheses. H0:H0: HA:HA: A Type I error in the context of this problem would be A Type II error in the context of this problem would be