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In: Statistics and Probability

In a large class of introductory Statistics​ students, the professor has each person toss a coin...

In a large class of introductory Statistics​ students, the professor has each person toss a coin 29 times and calculate the proportion of his or her tosses that were heads. Complete parts a through d below.

The Independence Assumption (is or is not) )_____satisfied because the sample proportions (are or are not)_____independent of each other since one sample proportion (can affect or does not affect)______another sample proportion. The​Success/Failure Condition is not satisfied because np=____ and nq=____which are both (less than or greater than or equal)_____ to 10

Range​ A, which corresponds to68%of the​ proportions, spans from ____ and ____.Range​ B, which corresponds to 95​%of the​ proportions, spans from _____ and ____. Range​ C, which corresponds to 99.7%of the​ proportions, spans from ___ and ____

About​ 68% of the students should have proportions between ___ and ____about​ 95% between _____and _____about​ 99.7% between ___ and ___

increased tosses to 75 The Independence Assumption (is or is not) )_____satisfied because the sample proportions (are or are not)_____independent of each other since one sample proportion (can affect or does not affect)______another sample proportion. The​Success/Failure Condition is not satisfied because np=____ and nq=____which are both (less than or greater than or equal)_____ to 10

Solutions

Expert Solution

Solution:

The Independence Assumption is satisfied because the sample proportions are independent of each other since one sample proportion does not affect another sample proportion. The​Success/Failure Condition is not satisfied because np=14.5 and nq=14.5 which are both greater than to 10

The empirical rule of the normal distribution is:

About 68% of the data lies within one standard deviation of the mean

About 95% of the data lies within two standard deviations of the mean

About 99.7% of the data lies within three standard deviations of the mean

The mean and standard deviation of the given data is:

Therefore, we have:

About 68% of the proportions lies between:

About 95% of the proportions lies between:

About 99.7% of the proportions lies between:

About​ 68% of the students should have proportions between 0.4072 and 0.5928 about​ 95% between 0.3144 and 0.6856 about​ 99.7% between 0.2216 and 0.7784

Increased tosses to 75

The Independence Assumption is satisfied because the sample proportions are independent of each other since one sample proportion does not affect another sample proportion. The​Success/Failure Condition is satisfied because np= 37.5 and nq=37.5 which are both greater than to 10

orchestra answered 2 years ago
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