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Consider each of the samples below and determine whether or not conditions are met to use a t-distribution for inference about the population mean. A.   B. C. D.  

Researchers test the provided hypotheses about two variables: ‘Favorite type of Apple’ (Red Delicious, Granny Smith, Honeycrisp, Empire, Gala) and ‘Time Aone where you Live: ‘(Pacific, Mountain, Central, Eastern) when based on a sample of n = 2000 U.S. adults. H0: There is no association between favorite type of apple and time zone where you live Ha: There is an association between favorite type of apple and time zone where you live Assume the researchers calculated a p-value of 0.0246.  What is the correct conclusion for this hypothesis test using a significance level of 0.05?

A  study considered the following two variables: 1. How many times went to the dentist in the past year: never or twice 2. Have a cavity:  no    yes     no yes total never 44  3  47 twice 49  4  53 total 93  7  100 Match the statistic to its corresponding calculation

Researchers surveyed n = 25 stat 200 male students to determine if they consume 3 or more alcoholic beverages per week. Their goal was to see if more than 50% of male students consume 3 or more alcoholic beverages per week. The relevant sample statistic is 0.60 (60%) with a standard error of 0.10.  The p-value is 0.159. Correctly complete the p-value interpretation below: The chance of seeing a test statistic of [answer1] = [answer2] or any value [answer3] is [answer4], if in fact the [answer5] hypothesis is true.

Researchers surveyed n = 25 stat 200 female students to determine how many days out of the week they consume one or more alcoholic beverage. Their goal was to see if there was evidence that females students in stat 200 had consumed alcoholic beverages more than 2 days per week, on the average. The relevant sample statistic is 2.30 days per week with a standard error of 0.332 days per week.  The p-value is 0.188. Correctly complete the p-value interpretation below: The chance of seeing a test statistic of [answer1] = [answer2] or any value [answer3] is [answer4], if in fact the [answer5] hypothesis is true.

:Assume a researcher asks 125 Penn State students the following two questions   How do you typically commute to class from your home? (walk, bike, take bus, drive) Are you an only child?  (yes, no) The responses are summarized below. Yes    No    Total Walk 25 35 60 Bike 6 12 18 Take the bus 4 18 22 Drive 10 15 25 Total 45 80 125 When considering ‘Yes’ and ‘Bike’,  the correct calculation for the expected count is [answer1]. The correct interpretation of the expected count is: If the two variables are [answer2], we would expect that around [answer3] of children who [answer4] an “only child” to [answer5] when commuting from home to class.

Does burning areas of an ecosystem improve the performance of native grasses? A team of ecologists tested this on 50 fields. Assume the researchers performed an experiment and calculated a p-value of 0.024.  Complete the statements below: Using a significance level of 0.05, the researchers should [answer1] the null hypothesis. It is possible that they have committed a type [answer2] error.

Consider the three histograms shown below. Each are based on n = 900 observations.   Match the histograms to the corresponding boxplots.

Consider the three histograms shown below. Each are based on n = 900 observations.   Match the histograms to the corresponding box plots.

We have access to the complete dataset of all ages (in years) at death for First Ladies of the U.S. who have passed. From this data set we know that the average age at death is 71.7 years. You are interested in how the sample statistics vary for different samples of size n=15 from this population.   A sampling distribution is constructed where one of the samples is used to create a bootstrap distribution.    This sample has mean: x-bar = 78 years. Below are boxplots of the sample of size n = 15, the sampling distribution, and the bootstrap distribution (although not necessarily in that order!).  Use all of the provided information to select the correct reason for each Boxplot identification. Boxplot A is the sample of n = 15 because it centered at the [answer5] where the sample standard deviation (s) is [answer6] the value of the standard error found with the sampling distribution. Boxplot B is the sampling distribution because it is centered at the [answer1] and has a standard error that is roughly equal to the estimated standard error found with the [answer2]. Boxplot C is the bootstrap distribution because it is centered at the [answer3] and has an estimated standard error that is roughly equal to the standard error found with the [answer4].