MAT 300 Unit 5 Milestone 5 Exam Answer Sophia Course

What is the standard error for this set of data?



2.63



7.65



2.77



8.1

2

Brad recorded the number of visitors at the local science museum during the week:

Tuesday: 18

Wednesday: 24

Thursday: 28

Friday: 30

He expected to see 25 visitors each day. To answer whether the number of visitors 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.



1.12



1.40



2.54



3.36

3

A school is gathering some data on its sports teams because it was believed that the distribution of boys and girls were evenly distributed across all the sports. This table lists the number of boys and girls participating in each sport.  

Boys Girls

Tennis 18 30

Soccer 42 15

Swimming 12 18

Select the observed and expected frequencies for the boys participating in soccer. 



Observed: 57

Expected: 24



Observed: 42

Expected: 22.5



Observed: 42

Expected: 24



Observed: 57

Expected: 22.5

4

The government claims that the average age of Californians is 34 years. Joe hypothesizes that the average age of the population of California is not equal to 34 years. He records a sample mean equal to 37 and states the hypothesis as  μ = 34 vs μ  ≠ 34. 

What type of test should Joe do? 



Two-tailed test



Right-tailed test



Joe should not do any of the types of tests listed 



Left-tailed test

5

A researcher has a table of data with 5 column variables and 4 row variables.

The value for the degrees of freedom in order to calculate the  statistic is __________.



20



19



12



4

6

What do the symbols , , and  represent?



Variables of interest



Sample statistics



Population parameters



Defined variables

7

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.



55.45 to 79.46



46.94 to 71.33



46.94 to 79.46



55.45 to 70.95

8

A table represents the number of students who passed or failed an aptitude test at two different campuses.

East Campus West Campus

Passed 39 45

Failed 61 55

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 East Campus and passed?



48.3 students



39 students



42 students



50.5 students

9

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 persons who took part in the survey, 71 are labeled as people who smoke regularly.

What is the standard error for the sample proportion?  Answer choices are rounded to the thousandths place. 



2.818



0.013



2.778



0.112

10

Select the statement that correctly describes a Type I error. 



A Type I error occurs when the null hypothesis is accepted when it is actually false.



A Type I error occurs when the null hypothesis is accepted when it is actually true.



A Type I error occurs when the null hypothesis is rejected when it is actually true.



A Type I error occurs when the null hypothesis is rejected when it is actually false.

11

The manager of a mall conducted a survey among two groups (n1 = 100, n2 = 100) of visitors to the mall on different days. She found that the first group spent an average of 60 minutes in the mall, while the second group spent an average of 90 minutes in the mall.

If the manager wishes to see the difference in the average times spent by the two groups in the mall, which of the following sets shows the null hypothesis and alternative hypothesis?



Null Hypothesis: There is no difference in the average times spent by the two groups in the mall.

Alternative Hypothesis: There is at least some difference in the average times spent by the two groups in the mall.



Null Hypothesis: There is at least some difference in the average times spent by the two groups in the mall.

Alternative Hypothesis: The difference in the average times spent by the two groups in the mall is 30 minutes.



Null Hypothesis: There is no difference in the average times spent by the two groups in the mall.

Alternative Hypothesis: There is a difference in the average times spent by the two groups in the mall, with a standard deviation of 30 minutes.



Null Hypothesis: There is at least some difference in the average times spent by the two groups in the mall.

Alternative Hypothesis: There is no difference in the average times spent by the two groups in the mall.

12

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.



1.645



1.220



1.555



1.175

13

Which of the statements about one-way ANOVA is FALSE?



The purpose of one way ANOVA is to verify whether the data collected from different sources converge on a common mean.



It is used when there are two independent variables in the experiment.



There can be any number of levels in one-way ANOVA.



ANOVA deals only with one factor, such as treatment or group.

14

A coin is tossed 50 times, and the number of times heads comes up is counted.

Which of the following statements about the distributions of counts and proportions is FALSE?



The distribution of the count of getting heads can be approximated with a normal distribution.



The distribution of the count of getting tails can be approximated with a normal distribution.



The count of getting heads is a binomial distribution.



The count of getting heads from a sample proportion of size 20 can be approximated with a normal distribution.

15

Which of the following is an example of a parameter?



Half of the receipts at the coffee shop include web address for giving feedback.



9047 out of 531,310 citizens voted in the special election for city council.



All of the members of the community watch group gave their availability to volunteer over the summer.



3.5% of the restaurant goers are given a survey to fill out.

16

Steven measures the weight of a random sample of 49 basset hounds. The mean weight was 45.8 pounds, with a standard deviation of 3 pounds. Using the alternative hypothesis that µ < 45.8, Steven found a z test statistic of -1.5.

What is the p-value of the test statistic?  Answer choices are rounded to the thousandths place.



0.134



0.055



0.067



0.147

17

One condition for performing a hypothesis test is that the observations are independent.  Mark is going to take a sample from a population of 400 students.  

How many students will Mark have to sample without replacement to treat the observations as independent?



40



300



80



360

18

The data below shows the grams of fat in a series of popular snacks.

If Morris wanted to construct a one-sample t-statistic, what would the value for the degrees of freedom be?



9



10



5



11

19

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.



-2.11



-2.34



-0.24



-0.03

20

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?



10



1



-1



-10

21

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.



-0.70



-1.44



-1.39



-2.87

22

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



4.489



2.896



2.998



2.517

23

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 persons who took part in the survey, 71 are labeled as people who smoke regularly.

What is the 90% confidence interval for this population proportion?  Answer choices are rounded to the hundredths place.



0.09 to 0.80



0.09 to 0.13



0.11 to 0.80



0.11 to 0.13

24

For a left-tailed test, the critical value of z so that a hypothesis test would reject the null hypothesis at 1% significance level would be __________.  Answer choices are rounded to the hundredths place.



-1.28



-2.33



-1.03



-3.09

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