b) According to a certain survey, adults spend 2.35 hours per day watching television on a weekday. Assume that the standard deviation for "time spent watching television on a weekday" is 1.93 hours. If a random sample of 60 adults is obtained, describe the sampling distribution of x overbar, the mean amount of time spent watching television on a weekday

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Sampling distribution

By the Central Limit Theorem, normally distributed, with mean 2.35 hours per day and standard deviation [tex]s = \frac{1.93}{\sqrt{60}} = 0.2492[/tex].

fichoh fichoh · Answer 2 · 2021-11-30T18:24:56+01:00

According to the central limit theorem, the mean and standard deviation of the sampling distribution are 2.35 and 0.249 respectively.

The sampling distribution :

The mean of the sampling distribution is estimated as being the same as the population mean based on the central limit theorem.

Hence, mean of sampling distribution, x = 2.35 hours

The standard deviation, s :

s = [tex] \frac{σ}{\sqrt{n}}[/tex]

Hence,

s = [tex] \frac{1.93}{\sqrt{60}} = 0.249[/tex]

Hence, the standard deviation of sampling distribution is 0.249

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