Question

According to American time use survey the typical American spends 154.8 minutes per day watching television. A random survey of 50 internet user results in a mean time watching television per day of 128.7 minutes with a sample standard deviation of 46.5 minutes test the claim that internet users spend less time watching television

Answer 1

There is enough evidence to support the claim that internet users spend less time watching television.

Explanation:

We are given the following in the question:

Population mean, μ = 154.8 minutes per day

Sample mean,
`\bar{x}` = 128.7 minutes

Sample size, n = 50

Alpha, α = 0.05

Sample standard deviation, s = 46.5 minutes

First, we design the null and the alternate hypothesis

`H_(0): \mu = 154.8\text{ minutes per day}\\H_A: \mu < 154.8\text{ minutes per day}}`

We use one-tailed t test to perform this hypothesis.

Formula:

`t_(stat) = \displaystyle\frac{\bar{x} - \mu}{(s)/(√(n)) }`

Putting all the values, we have

`t_(stat) = \displaystyle(128.7 - 154.8)/((46.5)/(√(50)) ) = -3.9689`

Critical Value:

Now,
`t_(critical) \text{ at 0.05 level of significance, 49 degree of freedom } = -1.6765`

Conclusion:

Since, the calculated test statistic is smaller than the critical value, we fail to accept the null hypothesis and reject it. We accept the alternate hypothesis.

Thus, there is enough evidence to support the claim that internet users spend less time watching television.