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Stacy recorded the number of minutes she used her
smartphone each day for one week before using an
app that awards points for decreased phone usage,
and for one week after using the app. Stacy's
alternative hypothesis is Ha:X< 114.6.
Before 103 127 87 12495 136 130
After 83 94 1201057598 96
Stacy used a simulation to randomize her data 200
times. She found that the difference between sample
means over 200 trials is approximately normally-
distributed, with a mean of -0.2 and a standard
deviation of 9.1. Which of the following conclusions
is most appropriate?
Phone use did not change.
Phone use increased and then decreased.
Phone use increased.
Phone use decreased.

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Using the t-distribution, the most appropriate conclusion for the hypotesis test is given by Phone use did not change.

How to find the value of z-statistic for population mean? (z test statistic)

Suppose we're specified that:

The sample mean = $$\overline{x}$$

The population mean =$$\mu$$

The population standard deviation = $$\sigma$$

The sample size = n

Then the z-statistic for this data is found as:

$$Z = \dfrac{\overline{x} - \mu}{\sigma/\sqrt{n}}$$

In this problem, the values of those parameters are as follows:

The sample mean $$\overline{x}$$ = -0.2

The population mean =$$\mu$$ = 0

The population standard deviation = $$\sigma$$ = 9.1

The sample size = n = 200

Hence, the test statistic is given by:

$$Z = \dfrac{\overline{x} - \mu}{\sigma/\sqrt{n}}\\\\\\Z = \dfrac{-0.2- 0}{9.1/\sqrt{200}}\\\\z = 0.31$$

Thus,

t = 0.31.

Since the absolute value of the test statistic is less than the critical value, we do not reject the null hypothesis and the conclusion is:

Phone use did not change.