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Tests of older baseballs showed that when dropped 24 ft onto a concrete surface, they bounced an average of 235.8 cm. In a test of 40 new baseballs, the bounce heights had a mean of 235.4 cm. Assuming a standard deviation of 4.5 cm, using a 0.05 significance level, what is the final conclusion?

a) Reject the null hypothesis
b) Fail to reject the null hypothesis
c) The P-value is inconclusive
d) There is not enough information to conclude

User Dule
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1 Answer

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Final answer:

b) Fail to reject the null hypothesis.

To determine whether the mean bounce height of the new baseballs is significantly different from the mean bounce height of the older baseballs, we can conduct a hypothesis test. After conducting the t-test and comparing the p-value to the significance level, we find that the p-value is greater than 0.05. Therefore, we fail to reject the null hypothesis.

Step-by-step explanation:

To determine whether the mean bounce height of the new baseballs is significantly different from the mean bounce height of the older baseballs, we can conduct a hypothesis test.

Our null hypothesis (H0) is that the mean bounce height of the new baseballs is equal to the mean bounce height of the older baseballs.

Our alternative hypothesis (Ha) is that the mean bounce height of the new baseballs is different from the mean bounce height of the older baseballs.

We can use a t-test to compare the means of two independent samples.

With a sample size of 40 and a known standard deviation of 4.5 cm, we can calculate the t-value and the p-value. Using a significance level of 0.05, we can compare the obtained p-value to determine the final conclusion.

After conducting the t-test and comparing the p-value to the significance level, we find that the p-value is greater than 0.05. Therefore, we fail to reject the null hypothesis.

The correct final conclusion is b) Fail to reject the null hypothesis.

This means that there is not enough evidence to conclude that the mean bounce height of the new baseballs is significantly different from the mean bounce height of the older baseballs.

User Angaj Sharma
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