## Related questions with answers

The TI-83/84 Plus calculator can be used to generate random data from a normally distributed population. The command randNorm(74, 12.5, 100) generates 100 values from a normally distributed population with $\mu=74$ and $\sigma=12.5$ (for pulse rates of women). One such generated sample of 100 values has a mean of $74.4$ and a standard deviation of 11.7. Assume that $\sigma$ is known to be $12.5$ and use a $0.05$ significance level to test the claim that the sample actually does come from a population with a mean equal to 74. Based on the results, does it appear that the calculator's random number generator is working correctly?

Solution

Verified$H_0:\mu=74$

$H_1:\mu\neq 74$

Determine the value of the test-statistic:

$z=\dfrac{\overline{x}-\mu}{\sigma /\sqrt{n}}=\dfrac{74.4-74}{12.5/\sqrt{100}}\approx 0.32$

Determine the corresponding P-value in table A-2:

$P=P(Z<-0.32\text{ or }Z>0.32)=2\times P(Z<-0.32)=2\times 0.3745=0.7490$

If the P-value is smaller than the significance level, reject the null hypothesis:

$P>0.05\Rightarrow \text{ Fail to reject } H_0$

There is not sufficient evidence to support the claim.

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