Assignment attached

Solution 10.2:
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In this study, the random variable of interest is the speed of pitches.
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Let be the mean speed of pitches from Wesley pitcher and be the mean speed of pitches from Rodriguez pitcher.
Here, the null hypothesis is that the mean speed of pitches from Wesley pitcher is equal to that of Rodriguez pitcher that is:
The alternative hypothesis is that the mean speed of pitches from Wesley pitcher is not equal to that of Rodriguez pitcher that is:
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The appropriate test will be two sample z-test as the population standard deviations are given here.
The z-test statistic is:
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The p-value corresponding to the two tailed z-test is 0.0140291.
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It can be observed that the p-value 0.0140291 is greater than the significance level 0.01 which implies that the null hypothesis cannot be rejected and it can be concluded that the mean speed of pitches from both pitchers is same.
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The population standard deviations are known.
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Let be the mean height of plants which are given the plant food and be the mean height of plants which are not given the plant food.
Here, the null hypothesis is that the mean height of plants which are given the plant food is equal to that of plants which are not given the plant food that is:
The alternative hypothesis is that the mean height of plants which are given the plant food is not equal to that of plants which are not given the plant food that is:
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The appropriate test will be two sample z-test as the population standard deviations are given here.
The z-test statistic is:
The p-value corresponding to the two tailed z-test is 0.0395918.
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The graph of p-value is given below:
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It can be observed that the p-value 0.04 is greater than the significance level 0.01 which implies that the null hypothesis cannot be rejected and it can be concluded that the mean height of both kind of plants is not different.
Solution 10.3:
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This is a test of proportions.
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The random variable is the number of OS1 system failures and OS2 system failures.
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Let be the proportion of OS1 system failures and be the proportion of OS2 system failures.
Here, the null hypothesis is that the be the proportion of OS1 system failures is equal to the proportion of OS2 system failures that is:
The alternative hypothesis is that the proportion of OS1 system failures is greater than the proportion of OS2 system failures that is:
.
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The p-value corresponding to the test statistic is 0.1008.
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It can be observed that the p-value 0.1008 is greater than the significance level 0.01 which implies that the null hypothesis cannot be rejected and it can be concluded that the proportion of OS1 system failures is not greater than the proportion of OS2 system failures
Solution 78:
Let be the mean number of English courses taken by males and be the mean number of English courses taken by females .
Null hypothesis:
Here, the null hypothesis is that the mean number of English courses taken by males is equal to the mean number of English...