Conduct the hypothesis test and provide the test statistic, critical value and P
ID: 3350144 • Letter: C
Question
Conduct the hypothesis test and provide the test statistic, critical value and P-Value, and state the conclusion. A person randomly selected 100 credit card purchases and recorded the cents portions of those amounts. The table below lists those cents portions categorized according to the indicated values. Use a 0.025 significance level to test the claim that the four categories are equally likely. The person expected that many checks for the whole dollar amounts would result in disproportionately high frequency for the first category, but do the results support that expectation?
Data set:
Cents portion 0-24 25-49 50-74 75-99
Number 51 23 11 15
Show all work:
The test statistic is __. (Round to three decimal places as needed).
The critical value is __. (round to 3 decimal places as needed).
The P-value is __. (Round to 4 decimal places a needed).
State the conclusion: ___ H 0 (below right).
There ___ sufficient evidence to warrant rejection of the claim that the 4 categories are equally likely.
The results ___ to support the expectation that the frequency for the first category is disproportionately high.
Explanation / Answer
test statisic; chisq = sum(Oi-Ei)^2/Ei = 39.040
critical value; chisq(.025,4-1) = 11.432
p-value; P(chisq>39.040;df=3) = 0.0000
with chisq = 39.040 and p-value< 0.025, i reject Ho at 2.5% leve of significance. AND conclude that the 4 categories are NOT equally likely
conclusion: Reject Ho.
There _IS__ sufficient evidence to warrant rejection of the claim that the 4 categories are equally likely.
The results _are statistically enough__ to support the expectation that the frequency for the first category is disproportionately high.
cents portion Oi pi = 1/4 Ei = pi*N (Oi-Ei)^2/Ei 0-24 51 0.25 25 27.04 25-49 23 0.25 25 0.16 50-74 11 0.25 25 7.84 75-99 15 0.25 25 4 sum = 39.040Related Questions
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