Statistics Questions

A college professor states that this year s entering students appear to be smarter than entering students from previous years The college s records indicate that the mean IQ for entering students from earlier years is 110 6 Suppose that we want to sample a small number of this year s entering students and carry out a hypothesis test to see if the professor s statement can be supported State the null hypothesis Ho and the alternative hypothesis H that we would use for this test LL 0 X O P S D

The mean height of a certain kind of plant is 141 centimeters Suppose we want to carry out a hypothesis test to see if the mean height when these plants are treated with a certain chemical differs from 141 State the null hypothesis Ho and the alternative hypothesis H that we would use for this test Ho D X P S

The age in human years H x of a dog that is x years old is modeled by the polynomial function H x 0 001183x4 0 05495x 0 8523 9 054x 6 748 where xz 1 Using the graph of this function shown below what is the approximately equivalent dog age for a person who is 70 Age in Human Years 100 80 8 60 40 20 Age of Dog years 15 20 OA B C D

ndard Normal Table Page 2 0 1 2 3 S 6 2 7 8 1 9 LO 1 2 3 4 L5 6 1 7 1 8 1 9 20 21 22 00 Standard Normal z Distribution Cumulative Area from the LEFT 5000 5398 5793 6179 6554 6915 7257 7580 7881 8159 8413 8643 8849 9032 9192 9332 9452 9554 9641 9713 9772 9821 9861 01 Click to view page 1 of the table Click to view page 2 of the table 5040 5438 5832 6217 6591 6950 7291 7611 7910 8186 8438 8665 8869 9049 9207 9345 9463 9564 9649 9719 9778 9826 9864 02 5080 5478 5871 6255 6628 6985 7324 7642 7939 8212 8461 8686 8888 9066 9222 9357 9474 9573 9656 9726 9783 9830 DOGO POSITIVE z Scores 03 5120 5517 5910 6293 6664 7019 7357 7673 7967 8238 8485 8708 8907 9082 9236 9370 9484 9582 9664 9732 9788 9834 04 5160 5557 5948 6331 6700 7054 7389 7704 05 5199 5596 5987 6368 6736 7088 7422 7734 8023 8289 8531 7995 8264 8508 8729 8749 8925 8944 9099 9115 9251 9265 9382 9394 9495 9505 9591 9599 9671 9678 9738 9744 9793 9798 9838 9842 06 5239 5636 6026 6406 6772 7123 7454 7764 8051 8315 8554 8770 8962 9131 9279 9406 9515 9608 9686 9750 9803 9846 07 5279 5675 6064 6443 6808 7157 7486 7794 8078 8340 8577 8790 8980 9147 9292 9418 9525 9616 9693 9756 9808 9850 08 5319 5714 6103 6480 6844 7190 7517 7823 8106 8365 8599 8810 8997 9162 9306 9429 9535 9625 9699 9761 9812 9854 09 5359 5753 6141 6517 6879 7224 7549 7852 8133 8389 8621 8830 9015 9177 9319 9441 9545 9633 9706 9767 9817 9857 X Standard Normal Table Page 1 NEGATIVE Z Scores 2 3 50 and lower 3 4 3 3 3 2 3 1 3 0 2 9 2 8 2 7 2 6 2 5 2 4 2 3 2 2 2 1 2 0 1 9 1 8 1 7 1 6 15 00 0001 0003 0005 0007 0010 0013 0019 0026 0035 0047 0062 0082 0107 0139 0179 0228 0287 0359 0446 0548 0668 01 Standard Normal z Distribution Cumulative Area from the LEFT 0003 0003 0005 0005 0007 0006 0009 0009 0013 0018 0025 0034 0045 0060 0080 0104 0136 0174 0222 02 0281 0351 0436 0537 ocer 03 0003 0004 0006 0009 0013 0012 0018 0017 0024 0023 0032 0043 0033 0044 0059 0078 0102 0132 0170 0217 0274 0344 0427 0526 0057 0075 0099 0129 0166 0212 0268 0336 0418 0516 and 04 0073 0096 0125 0162 0207 0262 0329 0409 05 0003 0004 0006 0008 0003 0004 0006 0008 0012 0011 0016 0023 0031 0041 0016 0022 0030 0040 0055 0054 0071 0094 0122 0158 0202 0256 0322 0401 andard 05050495 06 0003 0004 0006 0008 0011 0015 0021 0029 0039 0052 0069 0091 0119 0154 0197 0250 0314 0392 0485 70 07 0003 0004 0005 0008 0 0307 0384 0475 0003 0004 0005 0007 0011 0010 0015 0 0014 0021 0020 0027 0037 0049 0068 A 0066 0089 0087 0116 0113 0028 0038 0051 0150 0146 0192 0244 08 0188 0239 0301 0375 0465 C 0 0 0 01 01 01 02 02 030 04

Identify which of these types of sampling is used random systematic convenience stratified or cluster To determine her power usage Samantha divides up her day into three parts morning afternoon and evening She then measures her power usage at 4 randomly selected times during each part of the day What type of sampling is used O Cluster Systematic Random Convenience Stratified

QUESTION 1 1 POINT According to the latest financial reports from a sporting goods store the mean sales per customer was 75 with a population standard deviation of 6 The store manager believes 39 randomly selected customers spent more per transaction What is the probability that the sample mean of sales per customer is between 76 and 77 dollars 1 hour You may use a calculator or the portion of the z table given below Round your answer to two decimal places if necessary F Z 0 00 0 01 0 02 0 03 0 04 0 05 0 06 0 07 0 08 0 09 1 0 0 841 0 844 0 846 0 848 0 851 0 853 0 855 0 858 0 860 0 862 1 1 0 864 0 867 0 869 0 871 0 873 0 875 0 877 0 879 0 881 0 883 1 2 0 885 0 887 0 889 0 891 0 893 0 894 0 896 0 898 0 900 0 901 0

These are the heights of 20 individuals in inches Instructor Pranded Heights My owin Heights 60 62 63 65 66 66 67 70 71 72 73 63 64 66 67 69 71 72 74 79 Determine the mean and standard deviation for the 20 values using Excel Spread sheet Round statistics to two decurials

The probability density function of a continuous random variable X is given by 0 x 1 1 2 elsewhere T fx x 2 z 0 a What is the probablilty that X is between 1 and 2 b Find the expected value of X c Find the standard deviation of X 2 marks e Sketch or plot the PDF in the range 1 a 3 this must include all relevant features and labels 1 mark 1 mark 2 marks

Researchers are planning a study to estimate the impact on crop yield when no till is used in combination with residue retention and crop rotation Based on data from a meta analysis of 610 small farms the researchers estimate there is a 2 5 decline in crop yield when no till is used with residue retention and crop rotation Suppose the researchers want to produce a 95 confidence interval with a margin of error of no more than 1 0 Determine the minimum sample size required for this study The sample size needed to create a confidence interval estimate depends on the margin of error the initial estimated proportion and the confidence level Be sure to use proportions rather than percentages Round your final answer up to the nearest whole number n 14 field comparisons

Ten Initial Heights Use the following set of values along with 10 that you find yourself to create the data for the Weeks 5 7 labs PUT THESE 10 DATA VALUES IN THE EXCEL SPREADSHEET FIRST before adding your own 10 to the bottom of the list Heights in 60 63 65 66 66 67 70 71 72 73

Of the 13 500 savings accounts in a bank 4 675 belong to people younger than 40 years old The bank president would like to increase her institution s marketing strategy to younger customers so she is examining the population proportions in order to create a statistical study Find the population proportion as well as the mean and standard deviation of the sampling distribution for samples of size 400 n Round all answers to 3 decimal places Provide your answer below p

A baseball team calls itself America s Favorite Team because it has 90 000 fans on social media out of 2 210 000 social media users Find the population proportion as well as the mean and standard deviation of the sampling distribution for samples of size n 1 000 Round all answers to 3 decimal places Provide your answer below p

The owners of a baseball team are building a new baseball field for their team and must determine the number of seats to include The average game is attended by 6 500 fans with a standard deviation of 450 people Suppose a random sample of 10 games is selected to help the owners decide the number of seats to include Identify each of the following and be sure to round to the nearest whole number Provide your answer below U

The Washington Wheat Farmers Club is studying the impact of rising grain prices on their members planting habits The club members produce an average of 150 million bushels of wheat per year with a standard deviation of 18 million bushels The club takes a random sample of 35 years to create a statistical study Identify each of the following rounding the nearest hundredth when necessary Provide your answer below million bushels

A well known social media company is looking to expand their online presence by creating another platform They know that they current average 2 500 000 users each day with a standard deviation of 625 000 users If they randomly sample 50 days to analyze the use of their existing technology identify each of the following rounding to the nearest whole number if necessary Provide your answer below J n users users 1h

An organization has members who possess IQs in the top 4 of the population If IQs are normally distributed with a mear of 105 and a standard deviation of 15 what is the minimum IQ required for admission into the organization Use Excel and round your answer up to the nearest integer Provide your answer below

Two thousand students took an exam The scores are normally distributed with a mean of 81 points and a standard deviation of o 4 points Find the range of scores that represents the middle 50 Use Excel and round your answers to the nearest integer Provide your answer below

worn poorly set up machine is observed to produce components whose length X follows a normal distribution with a mean equal to 14 centimeters and a variance equal to 9 Determine the probability that a component is at least 12 centimeters long Round your answer to four decimal places Provide your answer below

A certain type of mango that weighs over 425 grams is considered to be large in size The weights for this type of mango X grams are normally distributed with a mean of 400 and a standard deviation of 25 Find the probability that a randomly selected mango of this type will not be considered as large size Round your answer to four decimal places Provide your answer below

Question A firm s marketing manager believes that total sales for next year will follow the normal distribution with a mean of 3 2 million and a standard deviation of 250 000 Determine the sales level that has only a 3 chance of being exceeded next year Use Excel and round your answer to the nearest dollar Provide your answer below

The weight of bags of green landscaping gravel X is modeled by normal distribution with a mean 26 7 kilograms and standard deviation 0 3 kilogram Determine the probability that a randomly selected bag of green gravel will weigh less than 26 kilograms Round your answer to four decimal places Provide your answer below

In a survey of men aged 20 29 in a country the mean height was 73 4 inches with a standard deviation of 2 7 inches Find the height of the shortest man in the top 10 Use Excel and round your answer to one decimal place Provide your answer below

A local utility company claims that the monthly electricity bills of its customers are among the lowest in the state with an average monthly electricity bill of 97 57 An energy analyst believes that the average monthly electricity bill from this utility company is actually higher than 97 57 The analyst collected a random sample of 41 monthly electricity bills from this utility company and found that the average monthly bill of the sample was 105 85 with a standard deviation of 18 76 Use the critical value method to test the hypothesis that the average monthly electricity bill for customers of this local utility is greater than 97 57 using a significance level of 1 State the null and alternative hypothesis for this test OH 97 57 H 97 57 O He p 97 57 H p 97 57 OH p 97 57 H 97 57 OH 97 57 H p 97 57 Determine the critical value for the hypothesis test 01 3031 02 7045 02 4232 01 6838 Determine the test statistic for the hypothesis test 01 3104 03 4030 02 8266 01 0053 Determine the appropriate conclusion for this hypothesis test O The sample data provide sufficient evidence to reject the alternative hypothesis that the average monthly electricity bill from this utility company is greater than 97 57 and thus we conclude that the average monthly electricity bill from this utility company is likely about 97 57 as claimed O The sample data do not provide sufficient evidence to reject the null hypothesis that the average monthly electricity bill from this utility company is 97 57 and thus we conclude that average monthly electricity bill from this utility company is likely about 97 57 O The sample data do not provide sufficient evidence to reject the alternative hypothesis that the average monthly electricity bill from this utility company is greater than 97 57 and thus we conclude that the average monthly electricity bill from this utility company is likely greater than 97 57 O The sample data provide sufficient evidence to reject the null hypothesis that the average monthly actocity bill from this utility company is 97 57 and thus we conclude that average monthly inah amater than 97 57

The times to complete an obstacle course is normally distributed with mean 73 seconds and standard deviation 0 9 seconds What is the probability using the Empirical Rule that a randomly selected finishing time is less than 100 seconds Provide the final answer as a percent rounded to two decimal places Provide your answer below

A Type 1 error is made when O the null hypothesis is not rejected when it was false O the null hypothesis is rejected when it was true O the alternative hypothesis is rejected when it was true O the alternative hypothesis is not rejected when it was false

Christopher has collected data to find that the total snowfall per year in Laytonville has a normal distribution What is the probability that in a randomly selected year the snowfall was greater than 53 inches if the mean u is 92 inches and the standard deviation o is 13 inches Use the empirical rule Provide the final answer as a percent rounded to two decimal places Provide your answer below

A college recently advertised that 86 of its students graduate debt free A student advocacy organization thinks that the college s claim is unlikely The organization collected a random sample of 1345 recent graduates from the college and found that 83 of the sample graduated without any student debt Use significance level of 1 and employ the critical value method to test the hypothesis that the proportion of all students from this college that graduate debt free is different than 86 State the null and alternative hypothesis for this test OH p 0 86 H p 0 86 H p 0 86 O He p20 86 OH p 0 86 H p 0 86 OH p0 86 H p 0 86 Determine the critical value s for the hypothesis test O 2 81 2 81 O 2 58 2 58 O 2 17 2 17 02 58 Determine test statistic for the hypothesis test 0 24 0 3 37 03 17 0 1 86 Determine the appropriate conclusion for this hypothesis test The sample data provide sufficient evidence to reject the alternative hypothesis that the proportion of all students at the college that graduate debt free is different than 0 86 and thus we conclude that the proportion of all students at the college that graduate debt free is likely equal to 0 86 The sample data do not provide sufficient evidence to reject the alternative hypothesis that the at the college that graduate debt free is different than 0 86 and thus we conclude that the proportion of all students at the college that graduate debt free is likely different The sample date de not provide sufficient evidence to reject the null hypothesis that the propertion of all students the college that graduate debt free is 0 06 and thus we conclude that the students at the college that graduate debt free is likely equal to 0 86 The sample data provide sufficient evidence to reject the null hypothesis that the proportion sun

if the confidence level of a confidence interval is decreased then the width of the confidence interval O increase sometimes but other times decrease O decrease O increase O remain constant

In a two tailed hypothesis test for a mean using a 0 03 a researcher calculated a p value of 0 1683 What conclusion can be drawn O The alternative hypothesis should be rejected since p a O The null hypothesis should be rejected since p a O The null hypothesis should not be rejected since p a O The null hypothessis is true 16 83 of the time

Two years ago a public health researcher found that 14 of American teens regularly vaped A different researcher would like to determine if the proportion of Americans that regularly vape has increased since State the appropriate null and alternative hypotheses for this test H p0 14 H p 0 14 H p 0 14 H p 0 14 OH p 0 14 OH p0 14 OH p 0 14 O He p 0 14

The width of a confidence interval is affected by the O Type I error O the population mean O sample size O the sample mean

The alternative hypothesis is a claim or statement about a O population parameter that will be declared true only if the null hypothesis is declared false O population parameter that is assumed true until it is declared false O population parameter that is assumed false until it is declared true O sample statistic that is assumed true until it is declared false

Find the area to the right of the z score 1 38 and to the left of the z score 1 53 under the standard normal curve Z 0 00 0 01 0 02 0 03 0 04 0 05 0 06 0 07 0 08 0 09 1 2 0 8849 0 8869 0 8888 0 8907 0 8925 0 8944 0 8962 0 8980 0 8997 0 9015 1 3 0 9032 0 9049 0 9066 0 9082 0 9099 0 9115 0 9131 0 9147 0 9162 0 9177 1 4 0 9192 0 9207 0 9222 0 9236 0 9251 0 9265 0 9279 0 9292 0 9306 0 9319 1 5 0 9332 0 9345 0 9357 0 9370 0 9382 0 9394 0 9406 0 9418 0 9429 0 9441 1 6 0 9452 0 9463 0 9474 0 9484 0 9495 0 9505 0 9515 0 9525 0 9535 0 9545 1 7 0 9554 0 9564 0 9573 0 9582 0 9591 0 9599 0 9608 0 9616 0 9625 0 9633 Use the value s from the table above Provide your answer below

Find the area under the standard normal curve between the z scores 0 94 and 0 76 Z 0 00 0 01 1 1 0 1357 0 1335 1 0 0 1587 0 1562 0 9 0 1841 0 1814 0 02 0 03 0 04 0 05 0 06 0 07 0 1314 0 1292 0 1271 0 1251 0 1230 0 1210 0 1539 0 1515 0 1492 0 1469 0 1446 0 1423 0 1788 0 1762 0 1736 0 1711 0 1685 0 1660 0 2061 0 2033 0 2005 0 1977 0 1949 0 1922 0 7 0 2420 0 2389 0 2358 0 2327 0 2296 0 2266 0 2236 0 2206 0 6 0 2743 0 2709 0 2676 0 2643 0 2611 0 2578 0 2546 0 2514 0 5 0 3085 0 3050 0 3015 0 2981 0 2946 0 2912 0 2877 0 2843 0 8 0 2119 0 2090 Use the value s from the table above Provide your answer below

A normal distribution is observed from the number of points per game for certain basketball player The mean for this distribution is 20 points and the standard deviation is 3 o points Use the empirical rule for normal distributions to estimate the probability that in a randomly selected game the player scored less than 26 points Provide the final answer as a percent rounded to one decimal place

A random sample of hybrid vehicle fuel consumptions has a sample mean of 53 2 mpg and sample standard deviation 4 8 mpg Use the Empirical Rule to estimate the percentage of hybrid vehicle fuel consumptions that are less than of s 43 6 mpg Round your answer to the nearest tenth jannunun

A random sample of small business stock prices has a sample mean of 54 82 and sample standard deviation of s 8 95 Use the Empirical Rule to estimate the percentage of small business stock prices that are more than 81 67 Round your answer to the nearest hundredth Provide your answer below

A random sample of adult reaction times has a sample mean of 394 3 milliseconds and a sample standard deviation of s 84 6 milliseconds Use the Empirical Rule to determine the approximate percentage of adult reaction times that lie between 140 5 and 648 1 milliseconds Round your answer to the nearest tenth Provide your answer below

A random sample of SAT scores has a sample mean of 1060 and sample standard deviation of s 195 Use the Empirical Rule to estimate the approximate percentage of SAT scores that are less than 865 Round your answer to the nearest whole number percent Provide your answer below

Suppose X N 6 5 1 5 and x 3 5 Find and interpret the z score of the standardized normal random variable Provide your answer below The z score when x 3 5 is The mean is This z score tells you that x 3 5 is standard deviations to the left of the mean 15 CAT P OFER Ih

Suppose X N 16 5 0 5 and 2 Provide your answer below www 16 Find and interpret the z score of the standardized normal random variable The z score when x 16 is The mean is This z score tells you that x 16 is standard deviation s to the left of the mean

Hugo averages 22 points per basketball game with a standard deviation of 4 points Suppose Hugo s points per basketball game are normally distributed Let X the number of points per basketball game Then X N 22 4 Provide your answer below Suppose Hugo scores 7 points in the game on Sunday The z score when x 7 is This z score tells you that x 7 is standard deviations to the left of the mean The mean is

Given the plot of normal distributions A and B below which of the following statements is true Select all correct answers Select all that apply B A

The graph below shows the graphs of several normal distributions labeled A B and C on the same axis Determine which normal distribution has the smallest standard deviation A C B 411

A and B below which of the following Statements is true Select all correct Answers B Select All that Apply A HAS the Larger Mean B HAS the Larger Mean The Means of A and B are equal A HAS the Larger Standard Deviation B HAS the Larger Standard Deviation The Standard Derations of A and Bare equal D

An index number provides a simple way to compare measurements made at different times or in different places The Cost of Living Index COLI is an index number used to compare expenses from one town or geographic region to another It is based on housing utilities grocery items transportation health care and miscellaneous goods and services 100 represent the national average The data sets below include the COLI rounded to the nearest whole number of four samples of six cities grouped by geographic region Which region has the least variation or spread Select the correct answer below Cost of Living Index Numbers COLI 119 82 101 100 75 73 77 79 67 72 58 65 96 64 80 73 64 66 75 78 76 71 70 65 Northeast Midwest West South E

The data sets below include four random sample of pulse rates in beats per minute Each sample includes the pulse rates for 7 individuals Use the Range Rule of Thumb to find an estimate for the standard deviation then determine which sample has the largest amount of variation Select the correct answer below Sample 1 Sample 2 Sample 3 Sample 4 64 78 54 102 76 86 56 100 90 70 70 78 70 94 70 66 50 72 66 64 54 78 36 102 68 66 56 70

Which of the data sets represented by the following box and whisker plots has the smallest standard deviation A B C H H 04 1

Body mass index BMI is a medical screening tool that measures body fat in an individual based on height and weight T following data sets include the BMI measurements for random samples of 7 individuals Use the range rule of thumb to estimate the standard deviation then determine which sample has the least amount of variation Select the correct answer below Sample 1 25 8 39 2 32 2 18 7 22 7 28 8 25 4 Sample 2 24 5 33 3 31 7 45 9 23 4 28 2 25 8 Sample 3 30 8 19 2 29 9 25 6 28 8 31 0 27 3 Sample 4 31 8 23 9 29 1 52 6 23 6 31 1 20 6

You are curious to see how strong of a correlation there is between the average temperature in your area and the total amount of popsicles you sell monthly Assume the data below is from 2022 Total number of popsicles sold Avg temp for the month in degrees F Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec 238 364 418 428 508 718 842 746 580 508 450 324 51 57 63 70 76 84 83 82 80 69 64 57 1 Using Microsoft Excel create a scatter plot with the data above Be sure to label your scatterplot Create a linear trendline line of best fit to go with your scatterplot Display the correlation coefficient r and the equation for the line of best fit on your scatter plot