Math  /  Data & Statistics

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You are conducting a multinomial hypothesis test (α=0.05(\alpha=0.05 ) for the claim that all 5 categories are equally likely to be selected. Complete the table. \begin{tabular}{|c|c|c|c|c|c|c|} \hline Category & Observed Frequency & \multicolumn{2}{|r|}{\begin{tabular}{l} Expected \\ Frequency \end{tabular}} & \multicolumn{3}{|l|}{(OE)2E\frac{(O-E)^{2}}{E}} \\ \hline A & 6 & 12.6 & & 3.457 & \checkmark & 0 \\ \hline B & 17 & 12.6 & & 1.537 & \checkmark & 080^{8} \\ \hline C & 6 & 12.6 & & 3.457 & \checkmark & 06 \\ \hline D & 16 & 12.6 & & 0.917 & \checkmark & 06 \\ \hline E & 18 & 12.6 & 0\checkmark 0 & 2.314 & \checkmark & 06 \\ \hline \end{tabular}
Report all answers accurate to three decimal places. But retain unrounded numbers for future calculations.
What is the chi-square test-statistic for this data? (Report answer accurate to three decimal places, and remember to use the unrounded Pearson residuals in your calculations.) χ2=11.6820\chi^{2}=11.682 \quad \checkmark 0^{\infty}
What are the degrees of freedom for this test? d.f. == \square 4 0
What is the pp-value for this sample? (Report answer accurate to four decimal places.) p -value = \square It may be best to use the =CHIDIST( ) function in a Spreadsheet to do this calculation. The pp-value is...

Studdy Solution

STEP 1

What is this asking? We're checking if people pick options A through E equally, and we need to calculate the chi-square test statistic, degrees of freedom, and p-value. Watch out! Don't round intermediate values, and make sure to use the right degrees of freedom!

STEP 2

1. Calculate the chi-square test statistic.
2. Calculate the degrees of freedom.
3. Calculate the p-value.

STEP 3

The chi-square test statistic is already calculated in the problem as the sum of the last column.
We're told it's χ2=3.457+1.537+3.457+0.917+2.314=11.682\chi^{2} = 3.457 + 1.537 + 3.457 + 0.917 + 2.314 = 11.682.

STEP 4

So the **chi-square test statistic** is χ2=11.682\chi^{2} = 11.682.

STEP 5

The degrees of freedom for a chi-square test is calculated as df=k1df = k - 1, where kk is the number of categories.

STEP 6

In this case, we have 5 categories (A, B, C, D, and E), so k=5k = 5.
Therefore, the degrees of freedom are df=51=4df = 5 - 1 = 4.

STEP 7

The p-value is the probability of observing a chi-square test statistic as extreme as, or more extreme than, the one calculated, assuming the null hypothesis is true (that all categories are equally likely).

STEP 8

We can use the `CHIDIST` function (as suggested) which takes the chi-square test statistic and degrees of freedom as input.
The function will return the p-value.

STEP 9

With χ2=11.682\chi^{2} = 11.682 and df=4df = 4, we get a p-value of 0.01970.0197.

STEP 10

The chi-square test statistic is χ2=11.682\chi^{2} = 11.682.
The degrees of freedom are 44.
The p-value is 0.01970.0197.

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