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What is the probability of a standard normal variable having a value between 0.5 and 2.5? Report your answer in decimal format with four decimal places, for example “0.1234”.  

A track coach claims that their new month-long training program will reduce the mile time by more than 1 minute. You want to statistically test the coach’s claim. You decide to randomly select 5 runners and record their mile times. You then have them follow the coach’s training program for a month and record their mile times post-training program. The times are listed below.   Subject Mile time Before Training Mile time After Training 1 6.7 5.0 2 7 5.8 3 6.2 4.9 4 8.5 7.2 5 9 7.6     This data could be appropriately analyzed using [color1],   We are interested in the hypotheses: [color2]. The degrees of freedom are [color3]  

Animal behavior researchers are interested in investigating if there is association between pet type and toy color. 229 pets were randomly selected out of a large population of cats and dogs. They asked these pets to choose a toy. Four different colors were available: red, blue, yellow, and green. The number of dogs and cats who selected each color is shown in the table below.  Red Blue Yellow Green Dogs 48 24 18 30 Cats 55 34 2 18 A Chi square test for independence was used to test the researchers claim.  Select the correct answer.

The distribution we use to find the p-value assumes…      

Eric wants to investigate the relationship between the number of tomatoes a plant produces and the number of aphids he finds on the plant. He takes a sample of five plants from his garden at random and gathers  the following data: Plant Number of tomatoes Number of Aphids 1 5 13 2 8 11 3 6 7 4 11 5 5 18 2 It appears that a straight line seems like a reasonable model for this data.  Note the following information: The mean number of aphids is 9.6. The SD of the number of aphids is 5.2 The mean number of tomatoes  is 7.6. The SD of the number of tomatoes is 4.4. The correlation between the number of aphids and the number of tomatoes is -0.85. a) Calculate the slope and intercept for a linear regression model with number of tomatoes as the response variable (2 points). b) Predict the number of tomatoes on a plant with 12 aphids  (2 points).

Regarding the Z and T distribution. Select all that apply. Note: Failure to select correct options or selecting incorrect ones will deduct points. 

Professor Tao has commissioned Ethan to investigate the population of Pokemon on Route 301. Ethan wanders around until he encounters 100 Pokemon on Route 301 (assume encountering a Pokemon is equivalent to drawing randomly from the population of Pokemon.) He catches each Pokemon he encounters and records its species: Pikachu Balbasaur Charmander Squirtle 20 19 26 35 Professor Tao thinks there should be an equal chance of finding each of the four species of Pokemon. Run a test for this hypothesis at the 1% significance level. Be sure to: a) state hypotheses (1 point) b) calculate the test statistic (2 points) c) calculate the p-value (1 point) d) draw conclusions, and interpret in context (1 point)

A scientist is comparing the mean weight of watermelons at two farms, farm A and farm B at a 5% significance level. He selected a random sample of 100 watermelons from farm A with a mean weight of 21.6 and a sample SD of 3.6 pounds. The random sample from farm B had 400 watermelons with a mean weight of 22.7 and a sample SD of 2.6 pounds.  Select the correct option in each case.  The appropriate test of significance the researcher should apply in this scenario is [color1] The appropriate standard error is [color2] The study type in this scenario is [color3]

A client arrives at the clinic for a pregnancy test. Her last menstrual period (LMP) was March 9, 2024. Her expected due date would be:

Ira has 20,000 or so citizens. Can Ira become a Home-Rule Municipality?