Harper MTH165 Homework Section 9.3 Latest 2020 MAY

MTH165 ELEMENTARY STATISTICS

Homework Section 9.3

In this section you learned how to test a hypothesis and compute a confidence interval for the difference in means for independent samples.

                In this section you are dealing with _____ __________________ data.

                The symbol for the parameter in this section is ___________.

                The symbol for the point estimate for that parameter is ______________.

                What input screen do you use for the interval estimate? ___

                What input screen do you use for the hypothesis test?  ___

Remember for bigger data sets you can copy and paste the columns of data into StatCrunch.

For smaller sets of data you should practice using your TI84 since that is the only technology you have available in the classroom when you take the departmental final exam.

Fill in the following as you work through your given problems in MyOpenMath

1.            a.) Hypothesis Test

                P:

H:

A:

Since quantitative information was collected from each object, we need to check the following conditions:

     Check all that apply.

The samples are independent

Normal populations or n1≥30 and n2≥30

no outliers for each group

σ is unknown for each group

There were not two measurements taken on the same object, so these samples are independent

Is the value of σ1 known? No

Is the value of σ2 known? No

Are there any outliers in data set 1? No, the modified boxplot of this data set shows no outliers

Are there any outliers in data set 2? No, the modified boxplot of this data set shows no outliers

n1 = 28 which is < 30

Is it reasonable to assume that population 1 is normally distributed? Yes, since the normal probability plot of data is roughly linear with no outliers.

n2 = 27 which is < 30

N:

T:

The symbol and value of the random variable on this problem are as follows:

     Round value to 2 decimal places

X?? - X?? = 50.78 km

t= 5.19

O:          

P value = 0.0000

                M:

Since the p-value ≤ 0.05, we reject H?.

S:

b.)          Confidence Interval

                P: already stated in part a

                A:already checked in part a

                N:

2-Sample T-Interval

I:

C:

2.            a.) Hypothesis Test

                P:

H:

A:

     Check all that apply.

The samples are independent

Normal populations or n1≥30 and n2≥30

no outliers for each group

σ is unknown for each group

There were not two measurements taken on the same object, so these samples are independent

Is the value of σ1 known? No

Is the value of σ2 known? No

Are there any outliers in data set 1? No, the modified boxplot of this data set shows no outliers

Are there any outliers in data set 2? No, the modified boxplot of this data set shows no outliers

n1 = 37 which is > 30

Is it reasonable to assume that population 1 is normally distributed? Not necessary to check since the sample size is at least 30.

 n2 = 37 which is > 30

Is it reasonable to assume that population 2 is normally distributed? Not necessary to check since the sample size is at least 30.

 N:

The conditions are met to use a 2-Sample T-Test

T:

The symbol and value of the random variable on this problem are as follows:

     Round value to 2 decimal places

 X?? - X?? = -15.52 cell phones per 100 residents

     Set up the formula of the test statistic with numbers rounded to 2 decimal place:

t= -2.37

O:

P value = 0.0103

M:

Since the p-value ≤ 0.04, we reject H?.

S:

There is significant evidence to conclude the mean number of cell phones per 100 residents of all countries of the Americas is less than the mean number of cell phones per 100 residents of all countries in Europe

b.)          Confidence Interval

                P: already stated in part a

                A: already checked in part a

                N: 2-Sample T-Interval

I:

C: