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MATH 300 Milestone 5 Answers Sophia answers/rationales_Fresh 2020/2021.

MAT 300 Milestone 5 Answers Sophia 1 Adam tabulated the values for the average speeds on each day of his road trip as 60.5, 63.2, 54.7, 51.6, 72.3, 70.7, 67.2, and 65.4 mph. The sample standard deviation is 7.309. Select the 98% confidence interval for Adam’s set of data. • 46.94 to 79.46 • 55.45 to 70.95 • 46.94 to 71.33 • 55.45 to 79.46 Confidence Intervals Using the T-Distribution 2 A table represents the number of students who passed or failed an aptitude test at two different campuses. South Campus North Campus Passed 42 31 Failed 58 69 In order to determine if there is a significant difference between campuses and pass rate, the chi-square test for association and independence should be performed. What is the expected frequency of South Campus and passed? • 50 students • 36.5 students • 42 students • 43.7 students CONCEPT Chi-Square Test for Homogeneity 3 Sukie interviewed 125 employees at her company and discovered that 21 of them planned to take an extended vacation next year. What is the 95% confidence interval for this population proportion? Answer choices are rounded to the hundredths place. • 0.10 to 0.23 • 0.16 to 0.17 • 0.11 to 0.16 • 0.11 to 0.21 CONCEPT Confidence Interval for Population Proportion 4 A market research company conducted a survey of two groups of students from different schools. They found that students from school A spent an average of 90 minutes studying daily, while the students from school B spent an average of 75 minutes daily. They want to find out if the difference in the mean times spent studying by the students of the two schools is statistically significant. Which of the following sets shows the correct null hypothesis and alternative hypothesis? • Null Hypothesis: There is no difference in the mean times spent by the schools' students. Alternative Hypothesis: There is at least some difference in the mean times spent by the schools' students. • Null Hypothesis: There is at least some difference in the mean times spent by the schools' students. Alternative Hypothesis: The students from school B spend more time studying than the students from school A. • Null Hypothesis: The difference in the mean times spent by the schools' students is 15 minutes. Alternative Hypothesis: There is no difference in the mean times spent by the schools' students. • Null Hypothesis: School B students spend more time studying than School A. Alternative Hypothesis: The difference in the mean times spent by the schools' students is 15 minutes. RATIONALE Recall that the null hypothesis is always of no difference. So the null hypothesis (Ho) is that the mean time studying for group A = mean for group B. This would indicate no difference between the two groups. The alternative hypothesis (Ha) is that there is difference in the mean study time between the two groups. CONCEPT Hypothesis Testing 5 Carl recorded the number of customers who visited his new store during the week: Day Customers Monday 17 Tuesday 13 Wednesday 14 Thursday 16 He expected to have 15 customers each day. To answer whether the number of customers follows a uniform distribution, a chi-square test for goodness of fit should be performed. (alpha = 0.10) What is the chi-squared test statistic? Answers are rounded to the nearest hundredth. • 0.40 • 1.60 • 0.67 • 2.33 CONCEPT Chi-Square Test for Goodness-of-Fit 6 Rachel measured the lengths of a random sample of 100 screws. The mean length was 2.9 inches, and the population standard deviation is 0.1 inch. To see if the batch of screws has a significantly different mean length from 3 inches, what would the value of the z-test statistic be? • 1 • 10 • -10 • -1 Then, getting the z-score we can note it is This tells us that 2.9 is 10 standard deviations below the value of 3, which is extremely far away. CONCEPT Z-Test for Population Means 7 What do the symbols , , and represent? • Sample statistics • Variables of interest • Population parameters • Defined variables CONCEPT Sample Statistics and Population Parameters 8 The data below shows the grams of fat in a series of popular snacks. Snack Grams of Fat Snack 1 9 Snack 2 13 Snack 3 21 Snack 4 30 Snack 5 31 Snack 6 31 Snack 7 34 Snack 8 25 Snack 9 28 Snack 10 20 If Morris wanted to construct a one-sample t-statistic, what would the value for the degrees of freedom be? • 10 • 9 • 11 • 5 CONCEPT T-Tests 9 A researcher has a table of data with 5 column variables and 5 row variables. The value for the degrees of freedom in order to calculate the statistic is __________. • 25 • 24 • 4 • 16 CONCEPT Pick Your Inference Test Chi-Square Test for Homogeneity Chi-Square Test for Association and Independence 10 Edwin conducted a survey to find the percentage of people in an area who smoked regularly. He defined the label “smoking regularly” for males smoking 30 or more cigarettes in a day and for females smoking 20 or more. Out of 635 people who took part in the survey, 71 are labeled as people who smoke regularly. Edwin wishes to construct a significance test for his data. He finds that the proportion of chain smokers nationally is 14.1%. What is the z-statistic for this data? Answer choices are rounded to the hundredths place. • -0.03 • -2.34 • -0.24 • -2.11 CONCEPT Z-Test for Population Proportions 11 Select the false statement about ANOVA. • If a researcher wants to compare the mean wages of females in different age groups at a particular company, he or she should not use an ANOVA because the population means are unknown. • If a researcher wants to study the effectiveness of three brands of nicotine patches, the researcher should use a One-Way ANOVA test. • A one-way ANOVA hypothesis test considers comparisons between populations based on one characteristic, while a two-way ANOVA hypothesis test considers comparisons between populations based on multiple characteristics. • If a researcher wants to compare the mean wages of females in different age groups at a particular company to the mean wages of males in different age groups at the same company, the researcher should use a Two-Way ANOVA test. CONCEPT One-Way ANOVA/Two-Way ANOVA 12 Rachel measures the lengths of a random sample of 100 screws. The mean length was 2.6 inches, with a standard deviation of 1.0 inches. Using the alternative hypothesis (µ < µ0), Rachel found that a z-test statistic was equal to -1.25. What is the p-value of the test statistic? Answer choices are rounded to the thousandths place. • 0.211 • 0.317 • 0.106 • 0.159 CONCEPT How to Find a P-Value from a Z-Test Statistic 13 The data below shows the heights in inches of 10 students in a class. Student Height, in inches Student 1 53 Student 2 52.5 Student 3 54 Student 4 51 Student 5 50.5 Student 6 49.5 Student 7 48 Student 8 53 Student 9 52 Student 10 50 The standard error of the sample mean for this set of data is __________. Answer choices are rounded to the hundredths place. • 1.77 • 0.59 • 0.19 • 1.87 RATIONALE CONCEPT Calculating Standard Error of a Sample Mean 14 For a left-tailed test, the critical value of z so that a hypothesis test would reject the null hypothesis at 10% significance level would be __________. Answer choices are rounded to the hundredths place. • -1.03 • -2.33 • -1.65 • -1.28 CONCEPT How to Find a Critical Z Value 15 One condition for performing a hypothesis test is that the observations are independent. Mary is going to take a sample from a population of 500 students. How many students will Mary have to sample without replacement to treat the observations as independent? • 300 • 50 • 490 • 100 CONCEPT Sampling With or Without Replacement 16 A market research company conducted a survey to find the level of affluence in a city. They defined the category "affluence" for males earning $100,000 or more annually and for females earning $80,000 or more annually. Out of 267 persons who replied to their survey, 32 are listed under this category. What is the standard error of the sample proportion? Answer choices are rounded to the hundredths place. • 1.96 • 0.20 • 0.02 • 0.32 CONCEPT Calculating Standard Error of a Sample Proportion 17 Joe hypothesizes that the average age of the population of Florida is less than 37 years. He records a sample mean equal to 37 and states the hypothesis as μ = 37 vs μ < 37. What type of test should Joe do? • Left-tailed test • Joe should not do any of the types of tests listed • Two-tailed test • Right-tailed test CONCEPT One-Tailed and Two-Tailed Tests 18 Adam tabulated the values for the average speeds on each day of his road trip as 60.5, 63.2, 54.7, 51.6, 72.3, 70.7, 67.2, and 65.4 mph. He wishes to construct a 98% confidence interval. What value of t* should Adam use to construct the confidence interval? Answer choices are rounded to the thousandths place. • 2.998 • 2.896 • 4.489 • 2.517 CONCEPT How to Find a Critical T Value 19 Which of the following is an example of a parameter? • Over 10,000 out of 15,000 citizens in a precinct participate in a special election. • Thirty randomly selected teens are asked about their average weekly hours spent on the Internet. • Fifty students in first grade have their heights taken to estimate average length. • All 450 students attending a school are asked to rank the quality of cafeteria food. CONCEPT Sample Statistics and Population Parameters 20 Maximus is playing a game. When he rolls the dice he wins if he gets an even number and loses if he gets an odd number. Which of the following statements is FALSE? • The count of rolling an odd number from a sample proportion size of 100 can be approximated with a normal distribution • The count of rolling an even number can be approximated with a normal distribution • Rolling an even number is considered a success • The count of rolling an odd number can be approximated with a normal distribution CONCEPT Distribution of Sample Proportions 21 A manufacturing company has two plants at different locations producing three different items. Based on the number of workers and the demand for the items in their respective locations, the number of items manufactured per day by each plant is listed in the table. Plant A Plant B Item 1 22 15 Item 2 8 12 Item 3 14 25 Select the observed and expected frequencies for Item 2 produced by Plant B. • Observed: 9.2 Expected: 10.8 • Observed: 9.2 Expected: 17.3 • Observed: 12 Expected: 17.3 • Observed: 12 Expected: 10.8 If each of these three options were evenly distributed among the 52 items produced by Plant B, we would need to divide the total evenly between the three options: This means we would expect 17.3 items from Plant B for each item 1, 2, and 3. CONCEPT Chi-Square Statistic 22 Ryan, a baker, measured the weights of cakes baked in each batch at his bakery and found that the mean weight of each cake is 500 grams. He performed a hypothesis test to find the mean weight of each cake by setting and . Select the statement that indicates a Type I error. • Rejecting the mean weight of each cake as 500 grams when . • Failing to reject the mean weight of each cake as 500 grams when . • Rejecting the mean weight of each cake as 500 grams when . • Failing to reject the mean weight of each cake as 500 grams when . Type I/II Errors 23 What value of z* should be used to construct an 88% confidence interval of a population mean? Answer choices are rounded to the thousandths place. • 1.175 • 1.645 • 1.220 • 1.555 CONCEPT Confidence Intervals 24 Adam tabulated the values for the average speeds on each day of his road trip as 60.5, 63.2, 54.7, 51.6, 72.3, 70.7, 67.2, and 65.4 mph. The sample standard deviation is 7.309. Adam reads that the average speed that cars drive on the highway is 65 mph. The t-test statistic for a two-sided test would be __________. Answer choices are rounded to the hundredths place. • -2.87 • -0.70 • -1.39 • -1.44

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