Bradley is returning home from a place that is 2 kilometers away. The function y = 2,000 − 90x represents Bradley's distance fro
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Answer:
Is plausible that the successive throws are independent
Step-by-step explanation:
1) Table with info given
The observed values are given by the following table
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First shot Made Second shot missed Total
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Made 152 33 185
Missed 37 8 45
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Total 189 41 230
2) Calculations and test
We are interested on check independence and for this we need to conduct a chi square test, the next step would be find the expected value:
Null hypothesis: Independence between two successive free throws
Alternative hypothesis: No Independence between two successive free throws
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First shot Made Second shot missed
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Made 189(185)/230=152.0217 41(185)/230=32.9783
Missed 189(45)/230=36.9783 41(45)/230=8.0217
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On this case all the expected values are higher than 5 and the sample size 230 is enough to apply the chi squared test.
3) Calculate the chi square statistic
The statistic for this case is given by:
Where O represent the observed values and E the expected values. Replacing the values that we got we have this
Now with the calculated value we can find the degrees of freedom
on this case r means the number of rows and c the number of columns.
Now we can calculate the p value
On this case the pvalue is a very large value and that indicates that we can fail to reject the null hypothesis of independence. So is plausible that the successive throws are independent.
Answer:
We conclude that less than or equal to 90% of all orders are mailed within 72 hours after they are received which means the company's claim is not true.
Step-by-step explanation:
We are given that the company claims that more than 90% of all orders are mailed within 72 hours after they are received. The quality control department at the company often takes samples to check if this claim is valid.
A recently taken sample of 175 orders showed that 161 of them were mailed within 72 hours.
<u><em>Let p = percentage of all orders that are mailed within 72 hours.</em></u>
SO, Null Hypothesis, : p
90% {means that less than or equal to 90% of all orders are mailed within 72 hours after they are received}
Alternate Hypothesis, : p > 90% {means that more than 90% of all orders are mailed within 72 hours after they are received}
The test statistics that will be used here is <u>One-sample z proportion</u> <u>statistics</u>;
T.S. = ~ N(0,1)
where, = proportion of orders that were mailed within 72 hours in a sample of 175 =
= 92%
n = sample of orders = 175
So, <u><em>test statistics</em></u> =
= 0.975
The value of the test statistics is 0.975.
<em>Now at 1% significance level, the z table gives critical value of 2.3263 for right-tailed test. Since our test statistics is less than the critical value of z as 0.975 < 2.3263, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which </em><em><u>we fail to reject our null hypothesis</u></em><em>.</em>
Therefore, we conclude that less than or equal to 90% of all orders are mailed within 72 hours after they are received which means the company's claim is not true.