Question

In the following problems , give a complete hypothesis test for each problem. Use the method described. Make sure you include the original claim in symbols, The null and alternative hypothesis, the significance level, the actual formula and calculation of the test statistic, give the p-value and a  drawing of critical region ,the decision concerning the null hypothesis and a conclusion stated in non technical terms

1. In a recent year, of the 109,857 arrests for Federal Offenses, 31968 were for drug offenses. Use a 0.01 significance level to test the claim that the drug offense rate is less than 30%.

2. In a previous test baseballs were dropped 24 ft. onto a concrete surface, and they bounced an average of 984 in. In a test of a sample of 40 new balls, the bounce heights had a mean of 92.67 in. with a standard deviation of 1.79 in. Use a 0.05 significance level to determine whether there is significant evidence to support the claim that the new balls have bounce heights with a mean different from 92.84.

3. A communications industry spokesperson claims that over 80% of Americans either own a smart phone or have a family member that does.  In a random survey of 1036 Americans, 956 said that they or a family member owns a smart phone. Test the spokesperson’s claim at the  level.

4. A large university says the mean number of classroom hours per week for full-time faculty is more than 9. A random sample of the number of classrooms hours for full-time faculty for one week is listed. At  test the university’s claim. Assume normality

10.7     9.8       11.6     9.7       7.6       11.3     14.1     8.1       11.5     8.5       6.9

5. USA Today ran a report about a University of North Carolina poll of 1248 adults from the southern United States. The poll asked them if they believed that Elvis was alive. 99 of the 1248 adults believed that Elvis still lives. The article began with the claim that almost 1 out of 10 Southerners still think Elvis is alive. At the 0.01 significance level, test the claim that the true percentage is less than 10%.

6. The FDA regulates that fish that is consumed is allowed to contain 1.0 mg/kg of mercury. In Florida, bass fish were collected in 53 different lakes to measure the amount of mercury in the fish. The data for the average amount of mercury in each lake is in table below Do the data provide enough evidence to show that the fish in Florida lakes has more mercury than the allowable amount? Test at the 10% level.

1.23	1.33		1.04		0.44		1.20		0.27
0.48	0.19		0.83		0.81		0.71		1.5
0.49	1.16		0.05		1.15		0.19		0.77
1.08	0.98		0.63		0.56		0.41		0.73
0.34	0.59		1.34		0.84		0.50		1.34
1.28	0.34		0.87		0.56		0.17		0.18
0.19	1.04		1.49		1.10		1.16		1.10
0.48	0.21		0.86		0.52		0.65		0.27
0.94		1.40		0.43		0.25		1.27

7. The Kyoto Protocol was signed in 1997, and required countries to start reducing their carbon emissions. The protocol became enforceable in February 2005. In 2004, the mean CO₂ emission was 4.87 metric tons per capita. The data below are a random sample of CO₂ emissions in 2010. Is there enough evidence to show that the mean CO₂ emission is lower in 2010 than in 2004? Test at the 1% level.

1.36	1.42		5.93	5.36		0.06	9.11		7.32
7.93	6.72		0.78	1.80		0.20	2.27		0.28
5.86	3.46		1.46	0.14		2.62	0.79		7.48
0.86		7.84			2.87			2.45

Answer 1

1.

Since p-value<0.01 so we reject H0 at 1% level of significance. Hence there is sufficient evidence to conclude that the drug offense rate is less than 30%.

2.

Since p-value>0.01 so we fail to reject H0 at 1% level of significance. Hence there is insufficient evidence to support the claim that the new balls have bounce heights with a mean different from 92.84.

(3)

Since p-value<0.01 so we reject H0 at 1% level of significance. Hence there is sufficient evidence to accept to claim that over 80% of Americans either own a smart phone or have a family member that does.

4.

Since Since p-value>0.05 so we reject H0 at 5% level of significance. Hence there is insufficient evidence to conclude the mean number of classroom hours per week for full-time faculty is more than 9.