### IHP 525 Quiz Two

- A telephone survey uses a random digit dialing machine to call subjects. The random digit dialing machine is expected to reach a live person 15% of the time.
- True or False: Each call is an independent random event.

In two attempts, what is the probability of achieving……

- exactly two successful calls? (success = reach a live person)
- one success and one failure (in any order)?

- The prevalence of a trait is 76.8%. In a simple random sample of
*n*= 50, how many individuals are expected to exhibit this characteristic and what is the corresponding standard deviation of this estimate?

- Linda hears a story on National Public Radio stating that one in six eggs in the United States are contaminated with
*Salmonella*. If*Salmonella*contamination occurs independently within and between egg cartons and Linda makes a three egg omelet, what is the probability that her omelet will contain at least one*Salmonella*contaminated egg?

- Suppose that heights of 10-year old boys vary according to a Normal distribution with µ = 138 cm and σ = 7 cm. What proportion of 10-year old boys is less than 140 cm in height?

- A survey selects a simple random sample of
*n*= 500 people from a town of 55,000. The sample shows a mean of 2.3 health problems per person. Based on this information, say whether each of the following statements is*true*or*false*. Explain your reasoning in each instance. No calculations necessary.

- It is reasonable to assume that the number of health problems per person will vary according to a normal distribution.
- It is reasonable to assume that the sampling distribution of the mean will vary according to a normal distribution.

- A simple random sample of 18 male students at a university has an average height of 70 inches. The average height of men in the general population is 69 inches. Assume that male height is approximately normally distributed with σ = 2.8 inches. Conduct a two-sided hypothesis test to determine whether the male students have heights that are significantly different than expected. Show all hypothesis testing steps.

- True or false? The
*p*-value refers to the probability of getting the observed result or something more extreme assuming the null hypothesis.

### IHP 525 Module Six Problem Set

- Hemoglobin levels in 11-year-old boys vary according to a normal distribution with σ=1.2 g/dL.
- How large a sample is needed to estimate µ with 95% confidence so the margin of error is no greater than 0.5 g/dL?

- A researcher fails to find a significant difference in mean blood pressure in 36 matched pairs. The test was carried out with a power of 85%. Assuming that this study was well designed and carried out properly, do you believe that there really is no significant difference in blood pressure? Explain your answer.

- Would you use a one-sample, paired-sample, or independent-sample
*t-test*in the following situations? - A lab technician obtains a specimen of known concentration from a reference lab. He/she tests the specimen 10 times using an assay kit and compares the calculated mean to that of the known standard.

- A different technician compares the concentration of 10 specimens using 2 different assay kits. Ten measurements (1 on each specimen) are taken with each kit. Results are then compared.

- In a study of maternal cigarette smoking and bone density in newborns, 77 infants of mothers who smoked had a mean bone mineral content of 0.098 g/cm
^{3}(*s*_{1}= 0.026 g/cm^{3}). The 161 infants whose mothers did not smoke had a mean bone mineral content of 0.095 g/cm^{3}(*s*_{2}= 0.025 g/cm^{3}). - Calculate the 95% confidence interval for µ
_{1}– µ_{2}. Get Nursing Report Writing Help!!

- Based on the confidence interval you just calculated, is there a statistically significant difference in bone mineral content between newborns with mothers who did smoke and newborns with mothers who did not smoke?

- A randomized, double-blind, placebo-controlled study evaluated the effect of the herbal remedy
*Echinacea purpurea*in treating upper respiratory tract infections in 2- to 11-year olds. Each time a child had an upper respiratory tract infection, treatment with either echinacea or a placebo was given for the duration of the illness. One of the outcomes studied was “severity of symptoms.” A severity scale based on four symptoms was monitored and recorded by the parents of subjects for each instance of upper respiratory infection. The peak severity of symptoms in the 337 cases treated with echinacea had a mean score of 6.0 (standard deviation 2.3). The peak severity of symptoms in the placebo group (n_{p}= 370) had a mean score of 6.1 (standard deviation 2.4). Test the mean difference for significance using an independent t-test. Discuss your findings.

# IHP 525 Module Five Problem Set

**Newborn weight.**A study takes a SRS from a population of full-term infants. The standard deviation of birth weights in this population is 2 pounds. Calculate 95% confidence intervals for μ for samples in which:- n = 81 and mean = 7.0 pounds
- n = 9 and mean = 7.0 pounds
- Which sample provides the most precise estimate of the mean birth weight?
- Interpret the CI you computed in part a).

**P-value and confidence interval.**A two-sided test of H0: μ = 0 yields a P-value of 0.03. Will the corresponding 95% confidence interval for μ include 0 in its midst? Will the 99% confidence interval for μ include 0? Explain your reasoning in each instance.

**Menstrual cycle length.**Menstrual cycle lengths (days) in an SRS of nine women are as follows: {31, 28, 26, 24, 29, 33, 25, 26, 28}. Use this data to test whether mean menstrual cycle length differs significantly from a lunar month using a one sample t-test. (A lunar month is 29.5 days.) Assume that population values vary according to a Normal distribution. Use a two-sided alternative. Show all hypothesis-testing steps.

**Menstrual cycle length.**Problem 3 calculated the mean length of menstrual cycles in an SRS of 9 women. The data revealed days with standard deviation s = 2.906 days.- Calculate a 95% confidence interval for the mean menstrual cycle length.
- Based on the confidence interval you just calculated, is the mean menstrual cycle length significantly different from 28.5 days at α = 0.05 (two sided)? Is it significantly different from μ = 30 days at the same α-level? Explain your reasoning. (Section 10.4 in your text considered the relationship between confidence intervals and significance tests. The same rules apply here.)

**Water fluoridation.**A study looked at the number of cavity-free children per 100 in 16 North American cities BEFORE and AFTER public water fluoridation projects. The table below lists the data. You will need to manually type the data into StatCrunch to use that tool to calculate the requested information.- Calculate delta values (After – Before) for each city. Then construct a stemplot or boxplot of these differences. Interpret your plot.
- What percentage of cities showed an improvement in their cavity-free rate?
- Estimate the mean change with 95% confidence (i.e. compute a 95% CI for the mean difference).