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27 June, 00:28

An increase in walking has been shown to contribute to a healthier life-style. A sedentary American takes an average of 5000 steps per day (and 65% of Americans are overweight). A group of health-conscious employees of a large health care system volunteered to wear pedometers for a month to record their steps. It was found that a random sample of 40 walkers took an average of 5430 steps per day, and the population standard deviation is 600 steps. At = 0.05 can it be concluded that they walked more than the mean number of 5000 steps per day?

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  1. 27 June, 00:58
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    Step-by-step explanation:

    We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean

    For the null hypothesis,

    H0: µ = 5000

    For the alternative hypothesis,

    H1: µ > 5000

    Since the population standard deviation is given, z score would be determined from the normal distribution table. The formula is

    z = (x - µ) / (σ/√n)

    Where

    x = sample mean

    µ = population mean

    σ = population standard deviation

    n = number of samples

    From the information given,

    µ = 5000

    x = 5430

    σ = 600

    n = 40

    z = (5430 - 5000) / (600/√40) = 4.53

    Looking at the normal distribution table, the probability corresponding to the z score is < 0.0001

    Since alpha, 0.05 > than the p value, then we would reject the null hypothesis. Therefore, at a 5% level of significance, it can be concluded that they walked more than the mean number of 5000 steps per day.
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