# Math assignment help

This is the first assignment to be submitted for module 7. I do expect to see how you work out the calculations in these problems. Due to the calculations involved, it may be easier to print the assignment and scan and upload as pdf files. You may upload up to 10 files. Another option is to take a digital photograph of the pages with the work completed and email or upload the pictures.

MAT 151

**M7A1**

**15 Points**

1. Collette is self-employed, selling items at Home Interior parties. She wants to estimate the average amount a client spends at each party. A random sample of 35 clients’ receipts gave a sample mean of $34.70 with population standard deviation $4.85.

1. Should you use the critical value (zc) or (tc) in determining a confidence interval in this problem? Explain.

2. Find a 90% confidence interval for the average amount expected to be spent by an individual.

3. Write a brief expanation of the meaning of the confidence interval in the context of this problem

4. For a party with 35 clients, use part (b) to estimate a range of dollar values for Collette’s total sales at that party.

2. How long does it take to commute from home to work? It depends on several factors including route, traffic, and time of departure. The data below are normally distributed results (in minutes) from a random sample of 8 trips.

27 | 38 | 30 | 42 | 24 | 37 | 30 | 39 |

1. Using technology, determine the mean for this data.

2. Using technology, determine the standard deviation for this data.

3. Should you use the critical value (zc) or (tc) in determining a confidence interval in this problem? Explain.

4. Use these data to create a 95% confidence interval for the population mean time of the commute.

3. A random sample of 53 students were asked for the number of semester hours they are taking this semester at Surry Community College. The sample standard deviation was found to be s = 4.7 semester hours. How many more students should be included in the sample to be 99% sure the sample mean is within one semester hour of the population mean for all students at this college? (Hint: the margin of error is the amount added or subtracted from the mean.)

4. How long do new batteries last on a camping trip? A random sample of n1 = 42 small camp flashlights were installed with brand I batteries and left on until the batteries failed. The sample mean lifetime was x1 = 9.8 hours with sample standard deviation s1 = 2.2 hours. Another random sample of n2 = 38 small flashlights of the same model were installed with brand II batteries and left on until the batteries failed. The sample mean of lifetimes was x2 = 8.1 hours with sample standard deviation s2 = 3.5 hours.

1. Should you use the critical value (zc) or (tc) in determining a confidence interval in this problem? Explain.

2. Find a 90% confidence interval for the population difference m1 – m2 of lifetimes for these batteries.

3. Does the confidence interval in part (b) contain all positive, all negative, or both positive and negative numbers? What does this tell you about the mean life of battery I compared to battery II?

5. Two pain relief drugs are being considered. A random sample of 8 doses of the first drug showed that the average amount of time required before the drug was absorbed into the bloodstream was x1 = 24 minutes with population standard deviation = 4 minutes. For the second drug, a random sample of 10 doses showed the average time required for absorption was x2 = 29 minutes with population standard deviation = 3.9 minutes. Assume the absorption times follow a normal distribution.

1. Should you use the critical value (zc) or (tc) in determining a confidence interval in this problem? Explain.

2. Find a 90% confidence interval for the difference in average absorption time for the two drugs.

3. Does it appear that one drug is absorbed faster than the other (at the 90% level)? Explain

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