11.1 Intro to Tests on Mean

What is the parameter of interest for this problem?

• p = the actual proportion of the stream that has a dissolved oxygen level below 5 mg/l.

• μ= the actual mean dissolved oxygen level of the stream.

• x-bar= the actual dissolved oxygen level of the samples of stream water.

• p-hat= the actual proportion of the sample that has a dissolved oxygen level below 5 mg/l.

What are the hypotheses for this test?

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Select 2 answers that correspond with checking the following conditions:

Random Condition Check: Pick the correct check of this condition.​ ​ ​

Normal Condition Check: Pick the correct check of this condition.​

• This was a random Sample
• This was not a random sample; Proceed with Caution
• The sample size is Large by the Central Limit Theorem, so this condition is satisfied.

• The population is Normally Distributed, so this condition is satisfied.

• The sample size is not Large by the Central Limit Theorem, but when you look at a graph (a boxplot or histogram) of the data, there are no signs of skewness or outliers, so this condition is satisfied (the t-procedure is robust enough for this situation).

Using the sample mean, x-bar = 4.771, and sample standard deviation, s = 0.9396, and sample size n = 15, calculate the test statistic for this problem. (In your calculator this can be done with a 1-sample t-test, labeled "t-test" in the Tests menu.)

• z = −0.94

• t = −0.94, df = 14

• t = 0.84, df = 14

If you were to have performed a 1 tail test at the α=0.05 significance level with the alternative hypothesis HA: μ > 31, with these data, would you have found evidence that the pineapples are larger?

• Yes, because the P-value would have provided sufficient evidence to reject the null hypothesis.

• Yes, because the P-value would not have provided sufficient evidence to reject the null hypothesis.