These are the only ones that I am having problems with. Please help..
8.You are given the sample mean and the sample standard deviation. Use this information to construct the 90% and the 95% confidence intervals for the population mean. Interpret the results and compare the widths of the confidence intervals. If convenient, use the technology to construct the confidence intervals
A random sample of 35 home theater systems has a mean price of $142.00 and a standard is $19.80
Construct a 90% confidence for the population mean:
The 90% confidence interval is
Construct a 95% confidence for the population mean:
The 95% confidence interval is
(Round to two decimals places as needed for both answers)
9. You are given the sample mean and the sample standard deviation. Use this information to construct the 90% and the 95% confidence intervals for the population mean. Which interval is wider? If convenient, use the technology to construct the confidence intervals
A random sample of 34 gas grills has the mean price of $649.30 and a standard deviation of $58.70
Construct a 90% confidence for the population mean:
The 90% confidence interval is
Construct a 95% confidence for the population mean:
The 95% confidence interval is
(Round to two decimals places as needed for both answers)
10.You are given the sample mean and the sample standard deviation. Use this information to construct the 90% and the 95% confidence intervals for the population mean. Which interval is wider? If convenient, use the technology to construct the confidence intervals
A random sample of 39 eight-ounce servings of different juice drinks has a mean of 79.4 calories and a standard deviation of 40.7 calories.
Construct a 90% confidence for the population mean:
The 90% confidence interval is ______________
Construct a 95% confidence for the population mean:
The 95% confidence interval is ___________
16. In a survey of 646 males ages 18 – 64, 392 say they have gone to the dentist in the past year.
Construct 90% and 95% confidence intervals for the population proportions. Interpret the results and compare the widths of the confidence intervals. If convenient, use technology to construct the confidence intervals.
The 90% confidence interval for the population proportion p is (____,_____)
(Round the final answers to the nearest thousandth as needed. Round all intermediate vales to the nearest thousandth as needed)
The 95% confidence interval for the population proportion p is (____,_____)
Interpret your results of both confidence intervals.
A. With the given confidence, it can be said that the population proportion or males ages 18-64 who say they have gone to the dentist in the past year is not between the endpoints of the given confidence interval.
B. With the given confidence, it can be said that the sample proportion or males ages 18-64 who say they have gone to the dentist in the past year is between the endpoints of the given confidence interval.
C. With the given confidence, it can be said that the population proportion or males ages 18-64 who say they have gone to the dentist in the past year is between the endpoints of the given confidence interval.
Which is wider?
The 90% confidence interval
The 95% confidence interval
You are given the sample mean and the sample standard deviation. Use this information to construct the 90% and the 95% confidence intervals for the population mean. Which interval is wider? If convenient, use the technology to construct the confidence intervals
A random sample of 34 gas grills has the mean price of $649.30 and a standard deviation of $58.70
Construct a 90% confidence for the population mean:
The 90% confidence interval is
Construct a 95% confidence for the population mean:
The 95% confidence interval is
To construct confidence intervals, you can use the following formulas:
For the confidence interval of the population mean:
Confidence interval = sample mean ± (critical value * standard deviation / sqrt(sample size))
For the confidence interval of the population proportion:
Confidence interval = sample proportion ± (critical value * sqrt((sample proportion * (1 - sample proportion)) / sample size))
Now let's solve the given problems step by step:
8. For the given sample of 35 home theater systems:
Sample mean = $142.00
Sample standard deviation = $19.80
To construct a 90% confidence interval for the population mean:
Critical value = 1.645 (you can look this value up in a t-table or use technology)
Confidence interval = $142.00 ± (1.645 * $19.80 / sqrt(35))
Confidence interval = $142.00 ± $6.96
Confidence interval = ($135.04, $148.96)
To construct a 95% confidence interval for the population mean:
Critical value = 1.96 (you can look this value up in a t-table or use technology)
Confidence interval = $142.00 ± (1.96 * $19.80 / sqrt(35))
Confidence interval = $142.00 ± $8.14
Confidence interval = ($133.86, $150.14)
The widths of the confidence intervals are $13.92 ($148.96 - $135.04) for the 90% confidence interval and $16.28 ($150.14 - $133.86) for the 95% confidence interval.
9. For the given sample of 34 gas grills:
Sample mean = $649.30
Sample standard deviation = $58.70
To construct a 90% confidence interval for the population mean:
Critical value = 1.69 (you can look this value up in a t-table or use technology)
Confidence interval = $649.30 ± (1.69 * $58.70 / sqrt(34))
Confidence interval = $649.30 ± $13.92
Confidence interval = ($635.38, $663.22)
To construct a 95% confidence interval for the population mean:
Critical value = 2.03 (you can look this value up in a t-table or use technology)
Confidence interval = $649.30 ± (2.03 * $58.70 / sqrt(34))
Confidence interval = $649.30 ± $16.72
Confidence interval = ($632.58, $666.02)
The widths of the confidence intervals are $27.84 ($663.22 - $635.38) for the 90% confidence interval and $33.44 ($666.02 - $632.58) for the 95% confidence interval.
10. For the given sample of 39 juice drinks:
Sample mean = 79.4 calories
Sample standard deviation = 40.7 calories
To construct a 90% confidence interval for the population mean:
Critical value = 1.69 (you can look this value up in a t-table or use technology)
Confidence interval = 79.4 ± (1.69 * 40.7 / sqrt(39))
Confidence interval = 79.4 ± 13.02
Confidence interval = (66.38, 92.42)
To construct a 95% confidence interval for the population mean:
Critical value = 2.03 (you can look this value up in a t-table or use technology)
Confidence interval = 79.4 ± (2.03 * 40.7 / sqrt(39))
Confidence interval = 79.4 ± 15.61
Confidence interval = (63.79, 95.01)
The widths of the confidence intervals are 26.04 (92.42 - 66.38) for the 90% confidence interval and 31.22 (95.01 - 63.79) for the 95% confidence interval.
16. For the survey of 646 males ages 18-64:
Sample proportion = 392/646 ≈ 0.606
Sample size = 646
To construct a 90% confidence interval for the population proportion:
Critical value = 1.645 (you can look this value up in a Z-table or use technology)
Confidence interval = 0.606 ± (1.645 * sqrt((0.606 * (1 - 0.606)) / 646))
Confidence interval = 0.606 ± 0.028
Confidence interval = (0.578, 0.634)
To construct a 95% confidence interval for the population proportion:
Critical value = 1.96 (you can look this value up in a Z-table or use technology)
Confidence interval = 0.606 ± (1.96 * sqrt((0.606 * (1 - 0.606)) / 646))
Confidence interval = 0.606 ± 0.033
Confidence interval = (0.573, 0.639)
The widths of the confidence intervals are 0.056 (0.634 - 0.578) for the 90% confidence interval and 0.066 (0.639 - 0.573) for the 95% confidence interval.
So, to answer your question about which intervals are wider:
- For the home theater systems (Question 8), the 95% confidence interval is wider than the 90% confidence interval.
- For the gas grills (Question 9), the 95% confidence interval is wider than the 90% confidence interval.
- For the juice drinks (Question 10), the 95% confidence interval is wider than the 90% confidence interval.
- For the survey of males ages 18-64 (Question 16), the 95% confidence interval is wider than the 90% confidence interval.
We do not do your homework for you. Although it might take more effort to do the work on your own, you will profit more from your effort. We will be happy to evaluate your work though.
However, I will start you out.
90% = mean ± 1.645 SEm
95% = mean ± 1.96 SEm
SEm = SD/√n