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Strike441 [17]
2 years ago
12

Lois bought clothing at a store. She did not have enough in her bank account to pay for the purchase. After receiving the bill a

nd paying off the balance, she realized that she paid $9.69 in interest. Which statement is true about her method of payment? Lois used a debit card to make the purchase. Lois used a credit card to make the purchase. Lois either used a debit card or used a credit card and paid the balance in full when the bill arrived. Lois either used a debit card or used a credit card and made a single payment.
Mathematics
2 answers:
fomenos2 years ago
8 0
<span>Lois used a credit card to make the purchase. 

One can't purchase an item that costs more than the balance in a debit card. The debit card is equivalent to cash on hand. You can only spend what you have. 

The credit card is equivalent to a loan. You don't have the money as of the moment but when you use the credit card, you owe the issuing bank the amount you've put on credit. The bank will pay the merchant and you will pay the bank. Interest is an additional expense when you pay your bill beyond the due date. The interest is applied on the amount outstanding upon the payment due date. </span>
timurjin [86]2 years ago
5 0

Answer:

b is the correct answer

Step-by-step explanation:

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Step-by-step explanation:

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To test whether or not there is a difference between treatments A, B, and C, a sample of 12 observations has been randomly assig
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Answer:

1. Null hypothesis: \mu_{A}=\mu_{B}=\mu_{C}

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2. D. 36

3. C. 34

4. B. 1.059

5. B. 8.02

Step-by-step explanation:

Analysis of variance (ANOVA) "is used to analyze the differences among group means in a sample".

The sum of squares "is the sum of the square of variation, where variation is defined as the spread between each individual value and the grand mean"

Part 1

The hypothesis for this case are:

Null hypothesis: \mu_{A}=\mu_{B}=\mu_{C}

Alternative hypothesis: Not all the means are equal \mu_{i}\neq \mu_{j}, i,j=A,B,C

Part 2

In order to find the mean square between treatments (MSTR), we need to find first the sum of squares and the degrees of freedom.

If we assume that we have p groups and on each group from j=1,\dots,p we have n_j individuals on each group we can define the following formulas of variation:  

SS_{total}=\sum_{j=1}^p \sum_{i=1}^{n_j} (x_{ij}-\bar x)^2

SS_{between}=SS_{model}=\sum_{j=1}^p n_j (\bar x_{j}-\bar x)^2

SS_{within}=SS_{error}=\sum_{j=1}^p \sum_{i=1}^{n_j} (x_{ij}-\bar x_j)^2

And we have this property

SST=SS_{between}+SS_{within}

We need to find the mean for each group first and the grand mean.

\bar X =\frac{\sum_{i=1}^n x_i}{n}

If we apply the before formula we can find the mean for each group

\bar X_A = 27, \bar X_B = 24, \bar X_C = 30. And the grand mean \bar X = 27

Now we can find the sum of squares between:

SS_{between}=SS_{model}=\sum_{j=1}^p n_j (\bar x_{j}-\bar x)^2

Each group have a sample size of 4 so then n_j =4

SS_{between}=SS_{model}=4(27-27)^2 +4(24-27)^2 +4(30-27)^2=72

The degrees of freedom for the variation Between is given by df_{between}=k-1=3-1=2, Where  k the number of groups k=3.

Now we can find the mean square between treatments (MSTR) we just need to use this formula:

MSTR=\frac{SS_{between}}{k-1}=\frac{72}{2}=36

D. 36

Part 3

For the mean square within treatments value first we need to find the sum of squares within and the degrees of freedom.

SS_{within}=SS_{error}=\sum_{j=1}^p \sum_{i=1}^{n_j} (x_{ij}-\bar x_j)^2

SS_{error}=(20-27)^2 +(30-27)^2 +(25-27)^2 +(33-27)^2 +(22-24)^2 +(26-24)^2 +(20-24)^2 +(28-24)^2 +(40-30)^2 +(30-30)^2 +(28-30)^2 +(22-30)^2 =306

And the degrees of freedom are given by:

df_{within}=N-k =3*4 -3 = 12-3=9. N represent the total number of individuals we have 3 groups each one with a size of 4 individuals. And k the number of groups k=3.

And now we can find the mean square within treatments:

MSE=\frac{SS_{within}}{N-k}=\frac{306}{9}=34

C. 34

Part 4

The test statistic F is given by this formula:

F=\frac{MSTR}{MSE}=\frac{36}{34}=1.059

B. 1.059

Part 5

The critical value is from a F distribution with degrees of freedom in the numerator of 2 and on the denominator of 9 such that we have 0.01 of the area in the distribution on the right.

And we can use excel to find this critical value with this function:

"=F.INV(1-0.01,2,9)"

And we will see that the critical value is F_{crit}=8.02

B. 8.02

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Step-by-step explanation:

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