Question

Math 203 Ch 8 Identify Worksheet Date 1. The U.S. Department of Commerce reports that 41.6% of Internet users preferred DSL as their method of service delivery. A random sample of 1000 Internet users shows 350 who preferred DSL Test whether the population proportion who prefer DSL has decreased, using level the 0.10 level of significance Underline the sentence or portion of the sentence that indicates the hypotheses. Identify the hypothesized population mean / proportion (with notation: Identify the sample mean/proportion (with notation: Identify the sample size (with notation: Identify the population or sample standard deviation with notation) or write N/A Identify the significance level (with notation: Determine the null & alternative hypothesis (using the notations): Determine if the test is left-tailed, right-tailed, or two-tailed: Determine the critical value: Determine the rejection regions: 2. A study found that subjects slept on average 20 minutes less on nights of the full moon than otherwise. Other researchers disagree and are interested in testing whether the mean difference in sleep is less than 20 minutes A random sample of 100 subjects showed that they slept, on average, 10 minutes less on nights of the full moon than otherwise. Assume the population standard deviation is 15 minutes. Use a 0.01 significance level. Underline the sentence or portion of the sentence that indicates the hypotheses Identify the hypothesized population mean/proportion (with notation): Identify the sample mean/proportion (with notation): Identify the sample size (with notation): Identify the population or sample standard deviation (with notation) or write N/A: Identify the significance level (with notation): Determine the null & alternative hypothesis (using the notations): Determine if the test is left-tailed, right-tailed, or two-tailed: Determine the critical value: Determine the rejection regions: 3. The National Traffic Highway Safety Commission keeps statistics on the mean years of potential life lost in alcohol-related fatal automobile accidents. For males, the mean years of life lost is 32. That is, on average, males involved in fatal drinking-and-driving accidents had their lives cut short by 32 years. A random sample of 36 alcohol-related fatal accidents had a mean years of life lost of 33.8, with a standard deviation of 6 years. Test whether the population mean years of life lost has increased at the 0.05 level Underline the sentence or portion of the sentence that indicates the hypotheses Identify the hypothesized population mean/proportion (with notation: Identify the sample mean / proportion (with notation: Identify the sample size (with notation: Identify the population or sample standard deviation with notation or write N/A Identify the significance level (with notation) Determine the null & alternative hypothesis (using the notations): Determine if the test is left-tailed, right-tailed, or two-tailed: Determine the critical value: Determine the rejection regions

Answer 1

1. Sample proportion who preferred DSL, p = 350/1000=0.350

Estimated proportion who prefer DSL, P = 0.416

Sample size, n = 1000

Level of significance, a (pronounced alpha) = 0.10.

Now, we will state the Null & Alternate Hypotheses as follows -

Null Hypothesis, Ho: p=P=0.416

Alternate Hypothesis, H1: p-P<0

Finding Standard Deviation, s, of the sampling distribution = {P*(1-P)/n}^0.5 = {0.416*0(1-0.416)/1000}^0.5 = 0.016

z-score =(p-P)/s = (0.35-0.416)/0.016 = -4.234

z-significant (corresponding to a=0.1) from the Z table = -1.28

Since our (negative) z-score is less than the (negative) z-significant value, we reject the null hypothesis. Therefore, we may say that the population proportion that prefers DSL has decreased.

Going further into the question, we can see that the 1st sentence of the question is the indicator of Null Hypothesis and the 2nd sentence tells about sample proportion from which we can get Alternate Hypothesis.

The Hypothesized population proportion is 0.416 as mentioned earlier in the answer and is denoted by P.

The sample proportion is 350/1000=0.350 as mentioned earlier in the answer and is denoted by p.

The sample size is 1000 and is denoted by n.

The population Standard Deviation is N/A while we can estimate the Standard Deviation of the sampling distribution as per the formula, s={P*(1-P)/n}^0.5.

The significance level as given in question is, a(pronounced as alpha) is 0.10.

The Null & Alternative Hypotheses are already defined earlier.

The test is a left tailed test as we are testing whether sample proportion is significantly less than the population (hence the Alternative Hypothesis has a less than operator).

The critical value is determined as z-significant earlier.

The rejection region is the entire region corresponding to the left of the z-significant point/value in the Normal Distribution Curve since our test is a left tailed test.