Most US adults have social ties with a large number of people, including friends, family, co-workers, and other acquaintances. It is nearly impossible for most people to reliably list all the people they know, but using a mathematical model, social analysts estimate that, on average, a US adult has social ties with people.1 A survey of randomly selected US adults who are cell phone users finds that the average number of social ties for the cell phone users in the sample was with a standard deviation of . Does the sample provide evidence that the average number of social ties for a cell phone user is significantly different from , the hypothesized number for all US adults?

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Most US adults have social ties with a large number of people, including friends, family, co-workers, and other acquaintances. It is nearly impossible for most people to reliably list all the people they know, but using a mathematical model, social analysts estimate that, on average, a US adult has social ties with 634 people.1 A survey of 1700 randomly selected US adults who are cell phone users finds that the average number of social ties for the cell phone users in the sample was 664 with a standard deviation of 778. Does the sample provide evidence that the average number of social ties for a cell phone user is significantly different from 634, the hypothesized number for all US adults?

The sample does not provide evidence that the average number of social ties for a cell phone user is significantly different from 634.

Explanation:

First, it is necessary to find out if the average number of social connections for a cell phone user is significantly different from 634 people. For this, we will consider:

H₀: The average number of social connections for a cell phone user is 634 people. For this we will use μ = 634.

Hₐ: The average number of social connections for a cell phone user is different from 634 people. For this we will use μ ≠ 634.

After these considerations we will adopt the following information:

n = 1700

'X = 664

SD = 778

We can see that the size of the sample is very large and as the population is unknown, we will use the concepts of the central limit theorem and adopt the average sample distribution in the same way as the normal distribution. For this reason, a single mean z test will be appropriate in this case.

After understanding the information, we can calculate the test value. For this it will be necessary to use the formula:

z= ('x-μ)/(SD/√n)

z =(664-663)/(778/√1700) = 1.59

When finding this value, you must take into account whether the p-value of the test is less than the significance level.

The p-value for the two-tailed test is found by the formula:

p - value = 2 * P (Z> 1.59)

p - Value = 2 [1-P (Z> 1.59)

p- value = 2 * (1-0.944) = 0.112

The p-test reveals a very high value in relation to the level of significance and shows that the null hypothesis must be rejected. Based on this, we can say that we have no factor that proves that the average number of social connections for a cell phone user is different from 634 people.

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