Statistics Questions and Answers

The length of Terry s fish is millimeters X e Terry caught a two year old flounder whose length had a z score of 0 6 How long was this fish Round the answer to at least one decima place G

Two high school statistics students are studying in their school s library They see the librarian seemingly selected random books from the shelves The two students wonder aloud what they believe the librarian is doing Student 1 states I bet she is selecting random books to try and find the average page number for the books in the library Student 2 states No I think she is selecting random books to estimate the proportion of books per category fiction non fiction etc Which student is correct

10 A large sample hypothesis test with known of a null hypothesis 15 against the alternative hypothesis 15 results in a test statistic of z 1 37 Assuming is known the corresponding p value is approximately Hint since is known we will use a z score with a normal distribution normalcdf A 0 0853 B 0 1707 C 0 4147 D 0 8293 E 0 9147

d Joachim a third student noted that the confidence interval in part a gives plausible values of the parameter as an interval between two values He suggested that they develop a one sided confidence interval because they were only concerned with whether the number 6 was landing face up more often than expected not less often The one sided interval will determine a value L such that all plausible 1 values of p are greater than L The formula for L is L p n i Determine the values of z needed to create the one sided 95 percent confidence interval Then calculate the value of L ii Do the results of Joachim s one sided confidence interval agree with results of Aurelia s significance test in part b Explain your reasoning

b Aurelia another student suggested they conduct a significance test to investigate the claim She tested the hypotheses Ho p versus Ha p at the significance level of a 0 05 She obtained a test statistic of 1 83 with a p value of 0 033 Do the results of the significance test agree with the results of Clarke s confidence interval in part a Explain your reasoning

22 22 What z scores are required for each percentage a 10 of the data is to the left of the z score Z score b 25 of the data is to the right of the z score z score

A residual plot indicates that a linear model is appropriate when it appears to be balanced and scattered be linear

MAP30 9 The ages of members in a hiking club are normally distributed with a mean of 25 and a standard deviation of 4 years a What percent of the members are older than 35 b If there were 80 members in the snowboarding club how many would be older than 35 205 000 and purchases a house in Saskatoon for 350 000 Round z scores

19 The ages of member a What percent of the members are older than b If there were 80 members in the snowboarding club how many would 20 Jennifer sells her house in Winnipeg for 305 000 and purchases a house in Saskatoon for 350 000 Round z sco to the nearest hundredth City Winnipeg Saskatoon Mean 286 000 346 000 Standard Deviation 7 150 1 600 a Given the house sale price determine the z score for Winnipeg b Given the house purchase price determine the z score for Saskatoon c Which house has the greater relative value Justify your answer

63 63 73 71 65 69 93 b What is the range for 95 of the data to c What is the range for 99 of the data to 17 The ages of members in a snowboarding club are normally distributed with a mean of 25 and a standard deviati 4 years 2 marks 18 a What percent of the members are younger than 20 b If there were 80 members in the snowboarding club how many would be under 20 years old The ages of members in a snowboarding club are normally distributed with a mean of 25 years and a sta deviation of 4 years 2 marks a What percent of the members are between 20 and 28 b If there were 80 members in the snowboarding club how many would be between 20 and 28

25 A manufacturer offers a 3 year warranty on its vacuum cleaners The vacuum cleaners have a mean lifespan of 4 5 years with a standard deviation of 0 5 years 3 marks a Determine the percentage of vacuum cleaners they would have to fix b If the company sold 100 000 vacuum cleaners how many would the company need to repair under warranty

Show your work 24 A manufacturer of mobile phones has determined that the phones require servicing after a mean of 30 months a standard deviation of 2 4 months What length of warranty should be offered if the manufacturer wants to repai less than 5 of the phones under the warranty 3 marks

7 A manufacture of plasma televisions has determined that the television require servicing after a mean of 67 months with a standard deviation of 7 2 months What length of warranty should be offered if the manufacturer wants to repair less than 3 of the televisions under the warranty 3 marks

An aquarium reports that guests mean visit time is 134 minutes Benjamin a dolphin trainer at the aquarium believes the mean visit time is not accurate for guests who visited in the past week Benjamin randomly surveys guests who visited the aquarium in the past week and receives 28 responses He calculates a sample mean of 137 minutes with a sample standard deviation of 3 5 minutes Conduct a significance test using a significance level of a 0 01 for the mean and make a conclusion 1 point 4 536 2 771 Benjamin rejects the null hypothesis The data suggests that the mean time for guests is not 134 minutes over the past week 4 454 2 771 Benjamin rejects the null hypothesis The data suggests that the mean time for guests is not 134 minutes over the past week 4 454 2 771 Benjamin fails to reject the null hypothesis The data suggests that the mean time for guests is 134 minutes over the past week 4 536 2 771 Benjamin fails to reject the null hypothesis The data suggests that the mean time for guests is 134 minutes over the past week

Previous Are the two matrices inverses answer will be yes or no 42 A 3 1 1 5 B 4 2

17 Determine the A matrix one would use to represent the following system of equations 2y 4s 2 3 12 1 3 0 2

14 Find the values of the variables 12 21 2 12 14 3 7 k 6 w 4 1 7 k 6 15 1 7 k 6 w 15 7 k 6 10 36

13 Select the answer to the problem below 3 5 3 2 3 3 12 15 8 1 3 3 16 B 17 12 D 8 10 Impossible 2 5 1 16 4

A particular residual y i is computed to be 5 In this case the predicted value is clearly an underestimation of the actual value an overestimation of the actual value

14 A teacher is analyzing the class results for a physics test The marks are normally dis with a mean u of 76 and a standard deviation of 4 Fill in the values at each standard deviation increment on the graph below Physics Test Marks 0 76 10 20 30 40 lo Mark 40 30 20

7 At the end of a bowling tournament three friends analyzed their scores Erinn s mean bowling score is 92 with a standard deviation of 8 Declan s mean bowling score is 130 with a standard deviation of 18 Matt s mean bowling score is 116 with a standard deviation of 33 28 Based on the means of their scores who appears to be the strongest bowler bom ost 251032 1 125 CoziH a Impossible to tell 8 00 b Declan CO 18 eg C Matt 38 d Erinn 8 Based on the standard deviation values of their scores which of the friends from Question 6 appears to be the most consistent bowler a Impossible to tell b Declan C Matt d Erinn

O Which description does not describe the graph of normally distributed data 052 129 291002 1251 gniwollo srl A2 E2 20 b c d a shaped like a bell starts off increasing then decreases symmetrical on either side of the mean starts off increasing and does not decrease SA with a mean of 40 an 02 84 88888 21

The least squares regression line will always pass through the coordinate mean of x random value of y mean of x mean of y random value of x mean of y

Skip The correlation coefficient is calculated by taking the sum of the products of each variable s standardized z scores and dividing that result by n 1 This means that r can only be negative can only be positive can be either positive negative or zero

A book publisher has fixed costs of 360 000 and variable costs per book of 9 00 The book sells 23 00 per copy How many books must be sold to break even If the fixed cost increased would the new break even point he higher or lower If the variable cost per unit decreased would the new break even point he higher or lower

By now You have used excel or Google sheets to graph data as it pertains to mass and volume Today you are going to revisit that practice Found below is the data acquired from a investigation much like the one that was turned in for the Microsoft Excel Lab Using the following data determine which of the following would most accurately describe the values of R squared and the equation for the trendline generated when graphing the data points Mass Volume 10 4 10 14 63 15 18 2 20 24 3 25 29 1 30 34 2 35 38 01 40 Equation y 1 05x 0 3259 R2 0 9965 Equation y 1 05x 0 3259 R2 0 7965 O Equation y 1 05x 0 3259 R2 0 9965 O Equation y 1 05x 0 3259 R 0 99999

For a set of bivariate data x 5 25 y 6 11 s x 1 22 s y 2 35 and r 0 7 The y intercept of the linear regression equation is 0 978 0 86

The table shows the height in feet of a projectile Number of Seconds 0 1 2 3 4 5 Height feet 10 12 13 12 8 4 Which quadratic regression equation BEST fits the data Ay 0 893x 3 236x 9 929 B y 0 893x 3 236x 9 929 y 0 5x 2 5x 10

What is the solution to the equation 9x 5 0 A B C z ti D 2 ti z 1 I 5 9 5 3 5 9 5

ST 5 What is the conjugate of 15 12 A 3 B 15 12 C 15 12 D 15 12

3 For this question choose TWO answers Which of the following expressions are equivalent to 9 187 i 9i 18 B 3 9i 7 211 2 3i D 9 1 2 E 81 9 6

Each year the high school guidance counselors conduct a survey to estimate the proportion of students at the high school who cheat on their homework Based on a random sample of 300 students from the high school a 99 confidence interval for the proportion of all students at the high school who cheat on their homework is 0 052 to 0 192 Name two changes the counselors could make to reduce the margin of error decrease the confidence level AND decrease the sample size increase the confidence level AND increase the sample size O decrease the confidence level AND increase the sample size

Each year the high school guidance counselors conduct a survey to estimate the proportion of students at the high school who cheat on their homework Based on a random sample of 300 students from the high school a 99 confidence interval for the proportion of all students at the high school who cheat on their homework is 0 052 to 0 192 Name two changes the counselors could make to reduce the margin of error decrease the confidence level AND decrease the sample size increase the confidence level AND increase the sample size O decrease the confidence level AND increase the sample size

Each year the high school guidance counselors conduct a survey to estimate the proportion of students at the high school who cheat on their homework Based on a random sample of 300 students from the high school a 99 confidence interval for the proportion of all students at the high school who cheat on their homework is 0 052 to 0 192 Describe how untruthful answers might lead to bias in this survey Does the margin of error account for this possible bias O The margin of error does NOT account for this bias Students may lie and say they don t cheat when they actually do O The margin of error DOES account for this bias Students may lie and say they don t cheat when they actually do O The margin of error does NOT account for this bias Students respond truthfully

A health magazine reported that 27 of adult males smoke cigarettes To test this claim they select 40 adult males at random and record if they smoke cigarettes They calculate a 95 confidence interval for the proportion of adult males who smoke and find it is 22 to 28 Based on the confidence interval is it plausible that the true proportion of adult males who smoke cigarettes is 27 Explain your answer Yes 27 falls outside the confidence interval No 27 falls outside the confidence interval Yes the confidence interval 0 22 to 0 28 contains the 27 claim O No the confidence interval 0 22 to 0 28 contains the 27 claim

A health magazine reported that 27 of adult males smoke cigarettes To test this claim they select 40 adult males at random and record if they smoke cigarettes They calculate a 95 confidence interval for the proportion of adult males who smoke and find it is 22 to 28 Calculate the point estimate and margin of error used to create the confidence interval Point Estimate Margin of Error Round your answer to the nearest hundredths

A population has a mean 158 and a standard deviation a 23 Find the mean and standard deviation of the sampling distribution of sample means with The mean is and the standard deviation is a Round to three decimal places as needed

Find the area of the shaded region under the standard normal curve Click here to view the standard normal table The area of the shaded region is Round to four decimal places as needed CITE

Assume the random variable x is normally distributed with mean 83 and standard deviation a 5 Find the indicated pro P 68 x 73 P 68 x 73 Round to four decimal places as needed

7 1 point A biologist wants to determine the effect of a new fertilizer on tomato plants What is the best design for this study 0000 Simulation Experiment Survey Observational Study

According to the Current Population Report of the United States census 16 7 of people aged 25 or older with a disability ha earned a bachelor s degree or higher Suppose that Nancy works for the city of Peoria AZ City officials have asked her to estimate the proportion of people aged 25 or older with a disability in Peoria who have earned a bachelor s degree or higher They have requested that her estimate have confidence level of 90 and a margin of error of 3 or 0 03 Determine the sample size n needed for the 90 confidence interval to be no more than 0 03 n 429 Incorrect people aged 25 or older with a disability Data obtained from the Current Population Reports from the United States Census 2015 Educational Attainment in the United States 2015 http www census gov content dam Census library publications 2016 demo p20 578 pdf accessed April 6 2016

4 For the polynomials in the first column determine the degree of each polynomial and tick the correct option Polynomial 884 686 83 12s 248 8 s 25 584 s 78 586 28 6 O O OOOOO 00000 c

Given the polynomial function z x 2 1 match each zero with its multiplicity 0 2 1 3 2 DRAG DROP THE ANSWE

9 What is the Quadratic Regression Formula Aya By mx b Cy ax bx c Y1 mx1 b

1 Question 1 14 Is this graph even or odd 2 ty Even B Odd 0 NEXT BOOKMARK

4 Heights of adult women have a mean of 63 6 in and a standard deviation of 2 5 in Does Chebyshev s Theorem say about the percentage of women with heights between 58 6 in and 68 6 in

1 A proud mother tells you that today her child is 1 209 600 s old What is the age of the child in days Show your work and make sure your answer has appropriate units U 03 U 05 U 13

Unit 5A Quadratic Inequality Remediation Assignment Maximum of 20 Points Highest grade a 70 Directions You can complete this assignment for a maximum of 20 points or a 70 In order to receive full credit all work must be shown The answers must be written in complete sentences You may choose 5 out of 7 problems 4 pts each Show all work and write your answer mathematically and in words DUE DATE Monday February 12 2024 during your class period NO LATE WORK ACCEPTED 1 A ball is thrown vertically upward with an initial velocity of 96 feet per second The distance s in feet of the ball from the ground after t seconds is s t 96t 16t a How many seconds will it take for the ball to strike the ground b Use interval notation to indicate the time s t where the ball is more than 128 feet above the ground 2 A scientist records the motion of a dolphin as it jumps from the water The function h t 16t 32t models the dolphin s height in feet above the water after t seconds Show all work and write your answer mathematically and in words Write and solve an inequality to determine when the dolphin is above 10 feet 3 A firework is shot straight up into the air with an initial velocity of 500 feet per second from 5 feet off the ground The function modeling the path of the firework is h t 16t 500t 5 where h t is the height in feet t seconds after it is shot in the air Show all work and write your answer mathematically and in words a At what time will the fireworks hit the ground b Write and solve an inequality that represents when the firework is at or above 2500 feet

If the variation in the residuals is less than the variation in the response variable then the model does not explain some of the variability in the response the model explains some of the variability in the response there is an error in process

10 1 point Which is an example of a continuous random variable Number of employees Defective pens Height of all sophomores Teachers at the conference 00