# Statistics Topics

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Statistics

StatisticsThe times it took to complete a frame of snooker were recorded at a tournament Here are the results times t mins freq f 0 t 10 11 10 t 20 30 20 t 30 45 30 t 60 14 O mid points m 0000 the mean time fm 6 mins

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StatisticsTwo months after the first flowers appear on a runner bean plant the lengths of the beans are all measured length 1 cm freq f 0 5 6 5 10 14 10 15 22 15 25 8 mid points m 6 fm

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StatisticsA group of people answer the question How many times did you shop at Ascobury s last week Here are the results visits v frequency f 0 1 2 3 4 Find the m 22 4 13 18 8 7 number of visits fv 5

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StatisticsA cashier answers the question How many of each of these notes do you have in the till Here are the results note value v 5 10 20 50 frequency fv f 27 25 36 12 Find the mean note value 0000 5

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ProbabilityThe manager of a computer retails store is concerned that his suppliers have been giving him laptop computers with lower than average quality His research shows that replacement times for the model laptop of concern are normally distributed with a mean of 4 1 years and a standard deviation of 0 6 years He then randomly selects records on 54 laptops sold in the past and finds that the mean replacement time is 3 8 years Assuming that the laptop replacement times have a mean of 4 1 years and a standard deviation of 0 6 years find the probability that 54 randomly selected laptops will have a mean replacement time of 3 8 years or less P M 3 8 years Enter your answer as a number accurate to 4 decimal places Based on the result above does it appear that the computer store has been given laptops of lower than average quality Yes The probability of this data is unlikely to have occurred by chance alone O No The probability of obtaining this data is high enough to have been a chance occurrence

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StatisticsThe data below was collected from manufacturer advertisements of their vehicles horsepower and highway gas mileage mpg Use this data to answer the following questions X y 190 220 158 250 340 350 390 15 17 11 35 42 33 28 1 Find the the correlation coefficient Round your final answer to four decimal places T 2 Write the regression equation below Round all numbers to four decimal places y 3 Using the data shown above predict the the highway gas mileage mpg for a car that has a horsepower of 225 Round your final answer to two decimal places 4 What percentage of variation in highway gas mileage mpg can be explained by horsepower Round your final answer to two decimal places

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ProbabilityRaven invested some money in an account The balance in the account is given by the equation B 7900 120t where t is the number of years since the initial investment was made and B is the account balance The equation tells us that Raven started with account is Select an answer at a rate of in the account and that the balance in the Select an answer

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StatisticsThe average resting heart rate of a population is 86 beats per minute with a standard deviation of 10 5 bpm Find the z scores that correspond to each of the following heart rates Round your answers to the nearest hundredth if necessary a 112 bpm Z b 67 bpm Z

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ProbabilityQuestion 3 Suppose the amount of time it takes a Capt Rig announcement to touch down is uniformly distri a Find the probability that for a randomly sele the plane after the announcement Round to 1 b What is the longest landing time included in

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StatisticsQuestion 2 0 6 pts 100 Pizza Co has recently received complaints about the inconsistent amount of cheese on their pizza Michelle the manager finds that the amount of cheese on a slice of pizza is uniformly distributed 6 ounces a Find the probability that there is less than 2 5 ounces of cheese on a slice of pizza Round to 3 places b Find the probability that there is at least 4 ounces of cheese on a slice of pizza Round to 3 dec places c Find the probability that there is between 2 75 to 3 25 ounces of cheese on a slice of pizza Ro decimal places d Find the 70th percentile for the amount of cheese on a slice of pizza This is the amount of ch is more than 70 of the of all slices e Find the average amount of cheese on a slice of pizza Round to 3 decimal places f Find the standard deviation for the amount of cheese on a slice of pizza Round to 3 decimal pl

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StatisticsThe following table shows results from a Polsson GLM generalized linear regression model testing the vocal behaviour of barn owl siblings number of calls while at the nest in response to three predictor variables Food treatment Parent sex and arrival time and interaction terms between some of these factors Link the correct statements below based on this information Intercept FoodTreatmentSatiated Arrival Time SexParentMale FoodTreatmentSatiated SexParentMale FoodTreatmentSatiated ArrivalTime Estimate Std Error 0 292 0 011 0 018 0 021 0 070 5 169 0 654 0 221 0 121 0 129 0 001 0 019 p value 0 004 0 001 0 039 0 001 0 065 0 978 When parents arrived earlier back to the nest Food treatment is a categorical variable with two options satiated and not satiated the models predicts satiated owls to make how many calls Tested interactions explore When the female parent arrived to the nest A owl sibblings made a similar number of calls B if the effect of food treatment on the number of calls varies depending on the sex of the parent and on the time of arrival C 5 823 calls D 5 169 calls E owl sibblings made significantly fewer calls F if the effect of parent sex on the number of calls varies when depending on the time of arrival G 0 654 calls owl gibblings made plan iesail

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StatisticsMoussa is investigating how long his phone s battery lasts in hours for various brightness levels on a scale of 0 100 His data is displayed in the table and graph below Brightness Level x Hours y 9 8 7 6 5 4 Hours 3 2 1 10 20 30 17 6 18 28 5 2 18 6 3 5 8 42 5 4 42 45 62 3 7 5 5 3 8 40 50 60 70 80 90 100 11 Brightness Level a What is the residual for the point 45 5 5 Round to 4 decimal places

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StatisticsModel Toxin ng Tail mm Residuals Min 1Q Median 3Q Max 61 958 8 286 3 026 16 246 38 771 Coefficients Intercept Tail mm QUESTION 18 Estimate 25 06 0 96 Signif codes 0 0 001 0 01 Std Error 8 675 0 049 0 05 0 11 t value 2 888 19 469 The 95 confidence interval for the regression model in Question 15 is as follows 2 5 0 86 97 5 1 06 Tail mm What is the range of expected toxin values in ng for a lizard with a tail length of 200 mm

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Statisticsule 6 and 7 Quiz for class K Claim Question 15 c Test the claim about the difference betwe samples are random and independent a H H x 0 10 Assume o o