Question

Asked Oct 16, 2019

In each of the following studies, a single samples mean is being compared to a population with a known mean but an unknown variance. For each study, decide whether thee result is significnt. (only a and b)

1 Rating

Step 1

**a)**

It is given that sample size is 16, sample mean (M) is 100.98, population mean is 100.31 and test is right tailed. The level of significance is 0.05.

Step 2

The hypotheses to be tested are:

*H*_{0}: *μ* =100.31, that is, true mean is equal to 100.31.

*H*_{a}: *μ* >100.31, that is, true mean is greater than 100.31.

Here, the population standard deviation, *σ*, is unknown; it is estimated by the sample standard deviation as, *s* = 2.00. So, in order to test whether the mean is greater than 100.31, the *t* test must be used.

The test statistic is found as follows:

Step 3

**p-value:**

For sample size *n*, the degrees of freedom (df) is *n* – 1. Here, df = 16 – 1 = 15.

The p-value using Excel formula “**=1–T.DIST(1.34,15,TRUE)”** is approximately 0.1001.

**Rejection rule:**

Reject the null hypothesis if p-value is less than the level of significance.

**Conclusion:**

The p-value is 0.1001 and the level of significance i...

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