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Class 9 Statistics Questions asked by Filo students

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If you draw a card with a value of four or less from a standard deck of cards, I will pay you

43. I f n o t, yo u p a y m e

10. (Aces are considered the highest card in the deck.) Step 2 of 2: If you played this game 755 times, how much would you expect to win or lose? Round your answer to two decimal places. Losses must be expressed as negative values.

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4) A machine that is calibrated to fill bags of coffee with 12 ounces is regularly checked to make sure it is filling bags appropriately. A quality control specialist samples 43 bags and finds a mean weight of 12.3 ounces and a standard deviation of 2.1 ounces. Do we have sufficient evidence to conclude that the machine is not filling the 12 oz bags appropriately? Perform a complete hypothesis test using alpha = 0.01. Identify the appropriate test, alpha, and check assumptions. Formulate hypotheses. Perform calculations (test statistic & p-value). Compare p-value to alpha and state conclusion. Write your conclusion.

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Suppose we are tossing two dice. Let A, B, and C denote the three events: "even number for the 1st outcome," "odd number for the 2nd outcome," and "same parity for the two outcomes," respectively. Here, 'parity' means both outcomes of the two dice are odd or both outcomes are even. Discuss whether the three events A, B, and C are independent or not.

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The Probability Mass Function, f(.), for the random variable X = {1, 2, 3, 4, 5} representing the number of daily computer failures is given as follows: x 1 2 3 4 5 f(x) 0.2 a 0.2 0.1 0.1 Determine the Cumulative Distribution Function of: 𝐹(4) − 𝐹(2.1) 0.4 0.5 0.2 0.1 0.3

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According to a recent poll of 2,000 adult Ukrainians, 1,600 of them support Ukraine's membership in the NATO alliance. Is there evidence that the proportion of all Ukrainians who support membership in NATO is significantly different from 85%? What is the null hypothesis?

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what is the probability of forming an even number if 3 digits number are made from the digits 1,2,3,5,6,8,9 and none of the digit are repeated.

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Texts: 2. (30 points) We want to compare the average airspeed velocity of an unladen European swallow to the average airspeed velocity of an unladen African swallow. To test this, a sample of n = 16 unladen European swallows was found to have an average airspeed velocity of μ = 8.4 m/s with a standard deviation of s = 0.25 m/s. The airspeed velocity of unladen swallows is known to be normally distributed. The average airspeed velocity of unladen African swallows is known to be 8.5 m/s. We want to test at 95% confidence if the average airspeed velocity of unladen European swallows is less than that of unladen African swallows. a) (10 points) Clearly write out the hypotheses. Ho: The average airspeed velocity of unladen European swallows is greater than or equal to the average airspeed velocity of unladen African swallows. Ha: The average airspeed velocity of unladen European swallows is less than the average airspeed velocity of unladen African swallows. b) (5 points) Decide on your test statistic and write out the formula. Support your answer. t-test The formula for the t-test is: t = (x̄ - μ) / (s / √n) where x̄ is the sample mean, μ is the population mean, s is the sample standard deviation, and n is the sample size. c) (10 points) Calculate your test statistic and P-value. Round to two decimal places. Test statistic: t = (8.4 - 8.5) / (0.25 / √16) = -0.40 / 0.0625 = -6.40 P-value = 0.0001 d) (5 points) Draw a conclusion. Since the P-value (0.0001) is less than the significance level of 0.05, we reject the null hypothesis. Therefore, there is sufficient evidence to conclude that the average airspeed velocity of unladen European swallows is less than the average airspeed velocity of unladen African swallows at a 95% confidence level.

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A certain lottery has 33 numbers. In how many different ways can 4 be selected? (Assume that order of selection is not important.)

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Find the area in the left tail more extremely than z = -2.50 in a standard normal distribution. Round your answer to four decimal places.

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Question 10

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Suppose two cubic centimeters of a paint spray cloud contains 77 spherical paint droplets, each having a typical radius of 6 micrometers. This paint cloud is overspray and is uniformly spread out in an auto body shop that has dimensions of 6 meters long, by 5 meters wide, by 4 meters high. How many cubic centimeters of paint are hanging in the air in this paint shop?

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Question 11

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(b) The area below 15 on a N (20, 2.9) distribution Round your answer to three decimal places.

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Question 12

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Which of the following claims about a normal distribution is correct: A normal distribution is used to describe continuous data. A normal distribution's mean can be symmetric or asymmetric. A normal distribution is defined by the values -1 and 1. All of the above

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Question 13

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If the odds against a horse winning a race is 5:11 , what is the probability of the horse winning the race? Express your answer as a simplified fraction.

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Question 14

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a) Hypotheses: Ho: There is no clear "favourite" among John, Paul, George, and Ringo. HA: There is a clear "favourite" among John, Paul, George, and Ringo. b) Test statistic: I used the chi-square test statistic (χ2) because we are comparing categorical data (the number of fans for each Beatle) to determine if there is a clear "favourite" among them. c) Calculation of test statistic: To calculate the chi-square test statistic, we need to compare the observed frequencies (O) with the expected frequencies (E) under the assumption of no preference. The formula for the chi-square test statistic is: χ2 = Σ((O - E)^2 / E) First, we need to calculate the expected frequencies. Assuming no preference, each Beatle would have an equal chance of being chosen, so the expected frequency for each Beatle would be 200/4 = 50. For John: (O - E)^2 / E = (57 - 50)^2 / 50 = 0.98 For Paul: (O - E)^2 / E = (55 - 50)^2 / 50 = 0.50 For George: (O - E)^2 / E = (48 - 50)^2 / 50 = 0.08 For Ringo: (O - E)^2 / E = (40 - 50)^2 / 50 = 2.00 Now, we sum up these values: χ2 = 0.98 + 0.50 + 0.08 + 2.00 = 3.56 Rounded to two decimal places, the test statistic is 3.56. d) Conclusion at 95% confidence (a = 0.05): To determine if there is a clear "favourite" among John, Paul, George, and Ringo, we compare the calculated test statistic (χ2 = 3.56) with the critical value from the chi-square distribution table. If the calculated test statistic is greater than the critical value, we reject the null hypothesis (Ho) and conclude that there is a clear "favourite." If the calculated test statistic is less than or equal to the critical value, we fail to reject the null hypothesis and conclude that there is no clear "favourite." Since the degrees of freedom for this test is 3 (number of categories - 1), the critical value for a chi-square test at 95% confidence level is 7.815. Since 3.56 < 7.815, we fail to reject the null hypothesis. Therefore, we conclude that there is no clear "favourite" among John, Paul, George, and Ringo based on the survey results.

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Question 15

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you can calculate a confidence interval for mu, if you have:

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Question 16

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ECMC Hospital has 15 patients arriving at the Emergency Unit on average per hour (assume these arrivals follow the Poisson distribution). What is the probability that exactly 4 patients will arrive during the next 20 minutes? Use e = 2.71828.

0.0065
0.05
0.0645
0.0690

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Question 17

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A random sample of registered nurses in a large hospital showed that they worked on average 43.5 hours per week. The standard deviation of 2.7 the sample was 12 . Estimate the mean of the population with confidence. Assume the variable is normally distributed. Round intermediate answers to at least three decimal places. Round your final answers to one decimal place.

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Question 18

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Translate the statement into a confidence interval. In a survey of 700 adults in a country, 78% think teaching is one of the most important jobs in the country today. The survey's margin of error is 3%.

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Question 19

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Texts: Application Exercise: A sociologist has assessed pollution and employment for some Canadian cities using a standard index. The sociologist predicts that more pollution is associated with more employment. What can be concluded with an 𝛼 of 0.01? pollution: 16 19 12 15 14 12 14 11 6 9 11 16 employment: 9 8 3 10 7 2 11 6 1 3 4 5 a) Select and compute the appropriate statistic. ---Select--- = b) Obtain/compute the appropriate values to make a decision about H0. Critical Value = ; Test Statistic = Decision: ---Select--- c) Compute the corresponding effect size(s) and indicate magnitude(s). If not appropriate, input and/or select "na" below. Effect Size = ; Magnitude: ---Select--- d) Make an interpretation based on the results. There was a significant positive relationship between pollution and employment. There was a significant negative relationship between pollution and employment. There was no significant relationship between pollution and employment.

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Question 20

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Given the probability that "she's up all night 'til the sun" OR "she's up all night for good fun" is 0.43, the probability that "she's up all night for good fun" is 0.11, and the probability that "she's up all night 'til the sun" AND "she's up all night for good fun" is 0.26, what's the probability that "she's up all night 'til the sun"? Round to 2 decimal places as needed.

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