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3 years ago

The mean of a sample

Mathematics

1 answer:

hammer [34]3 years ago

6 0

Answer:

c. is computed by summing all the data values and dividing the sum by the number of items.

Step-by-step explanation:

Mean is said to be the average of the entire data set. Even in case when data set is too large we choose to calculate the mean of sample. In that case, sum up all the data of sample and divide by the number of items.

For example:

There are 50 students in the class, but some students are not present, some are not in the class, to collect information from all students is not feasible, in that case.

The data of some random 10 students is taken, example to check the proficiency in mathematics their scores in last class test are summed up, and divided by number of students considered.

That is sum of marks obtained by 10 students divided by 10, will provide the mean.

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$z=\frac{0.75 -0.72}{\sqrt{\frac{0.72(1-0.72)}{900}}}=2.00$

Now we can calculate the p value. Since is a bilateral test the p value would be:

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Step-by-step explanation:

Information given

n=900 represent the random sample selected

$\hat p=0.75$ estimated proportion of residents favored annexation

$p_o=0.72$ is the value that we want to test

represent the significance level

z would represent the statistic

$p_v$ represent the p value

Hypothesis to test

The political strategist wants to test the claim that the percentage of residents who favor annexation is above 72%.:

Null hypothesis: $p\leq 0.72$

Alternative hypothesis: $p > 0.72$

The statistic for this case is given by:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)

Replacing the data given we got:

$z=\frac{0.75 -0.72}{\sqrt{\frac{0.72(1-0.72)}{900}}}=2.00$

Now we can calculate the p value. Since is a bilateral test the p value would be:

$p_v= P(Z>2) =0.0228$

Since the p value is lower than the significance level of 0.05 we have enough evidence to conclude that the true proportion of residents favored annexation is higher than 0.72 or 72%

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3 years ago