The personnel office at a large electronics firm regularly schedules job interviews and maintains records of the interviews. From the past records, they have found that the length of a first interview is normally distributed, with mean μ = 36 minutes and standard deviation σ= 4 minutes. (Round your answers to four decimal places.)

(a) What is the probability that a first interview will last 40 minutes or longer?


(b) Three first interviews are usually scheduled per day. What is the probability that the average length of time for the three interviews will be 40 minutes or longer?

Last year's records of auto accidents occurring on a given section of highway were classified according to whether the resulting damage was $1,000 or more and to whether a physical injury resulted from the accident. The data follows.

(a) Estimate the true proportion of accidents involving injuries when the damage was $1,000 or more for similar sections of highway. (Round your answer to three decimal places.)


Find the 95% margin of error. (Round your answer to three decimal places.)


(b) Estimate the true difference in the proportion of accidents involving injuries for accidents with damage under $1,000 and those with damage of $1,000 or more. Use a 95% confidence interval. (Use p₁ − p₂ where p₁ is the proportion of accidents involving injuries with damage under $1,000 and p₂ is the proportion of accidents involving injuries with damage of $1,000 or more. Round your answers to three decimal places.)

Healthcare administration leaders are asked to make evidence-based decisions on a daily basis. Sometimes, these decisions involve high levels of uncertainty, as you have examined previously. Other times, there are data upon which evidence-based analysis might be conducted. This week, you will be asked to think of scenarios where building and interpreting confidence intervals (CIs) would be useful for healthcare administration leaders to conduct a two-sided hypothesis test using fictitious data. For example, Ralph is a healthcare administration leader who is interested in evaluating whether the mean patient satisfaction scores for his hospital are significantly different from 87 at the .05 level. He gathers a sample of 100 observations and finds that the sample mean is 83 and the standard deviation is 5. Using a t-distribution, he generates a two-sided confidence interval (CI) of 83 +/- 1.984217 *5/sqrt(100). The 95% CI is then (82.007, 83.992). If repeated intervals were conducted identically, 95% should contain the population mean. The two-sided hypothesis test can be formulated and tested just with this interval. Ho: Mu = 87, Ha: Mu<>87. Alpha = .05. If he assumes normality and that population standard deviation is unknown, he selects the t-distribution. After constructing a 95% CI, he notes that 87 is not in the interval, so he can reject the null hypothesis that the mean satisfaction rates are 87. In fact, he has an evidence-based analysis to suggest that the mean satisfaction rates are not equal to (less than) 87.

Consider how a CI might be used to support hypothesis testing in a healthcare scenario. Post a description of a healthcare scenario where a CI might be used, and then complete a fictitious two-sided hypothesis test using a CI and fictitious data.

Think about a population mean that you may be interested in and propose a hypothesis test problem for this parameter. Gather appropriate data and post your problem, Also, post your own solution at the end.

For example, you may believe that the population mean number of times that adults go out for dinner each week is less than 1.5. Your data could be that you spoke with 7 people and found that they went out 2, 0, 1, 5, 0, 2, and 3 times last week. You then would choose to test this hypothesis at the .05 (or another) significance level. Assume a random sample.

Professor Fair believes that extra time does not improve grades on exams. He randomly divided a group of 300 students into two groups and gave them all the same test. One group had exactly 1 hour in which to finish the test, and the other group could stay as long as desired. The results are shown in the following table. Test at the 0.01 level of significance that time to complete a test and test results are independent.

(i) Give the value of the level of significance.


State the null and alternate hypotheses.

H₀: The distributions for a timed test and an unlimited test are different.
H₁: The distributions for a timed test and an unlimited test are the same.H₀: The distributions for a timed test and an unlimited test are the same.
H₁: The distributions for a timed test and an unlimited test are different.    H₀: Time to take a test and test score are not independent.
H₁: Time to take a test and test score are independent.H₀: Time to take a test and test score are independent.
H₁: Time to take a test and test score are not independent.

(ii) Find the sample test statistic. (Round your answer to two decimal places.)


(iii) Find or estimate the P-value of the sample test statistic.

P-value > 0.1000.050 < P-value < 0.100    0.025 < P-value < 0.0500.010 < P-value < 0.0250.005 < P-value < 0.010P-value < 0.005

(iv) Conclude the test.

Since the P-value < α, we do not reject the null hypothesis.Since the P-value < α, we reject the null hypothesis.    Since the P-value is ≥ α, we do not reject the null hypothesis.Since the P-value ≥ α, we reject the null hypothesis.

(v) Interpret the conclusion in the context of the application.

At the 1% level of significance, there is insufficient evidence to claim that time to do a test and test results are not independent.At the 1% level of significance, there is sufficient evidence to claim that time to do a test and test results are not independent.

Discuss how the concepts of Applied Biostatistics can be applied to real-world situations and increase your chances of career or life success.

In the survey of 1500 students for the united states age 18 and under, 1043 were concerned about how they would pay for college.

a) Find the mean and standard deviation of those concerned about financing college.

b) Construct a 90% confidence interval for the population proportions. Interpret your results.

c) Find the minimum sample size needed to estimate the population proportion at the 99% confidence level in order to ensure that the estimate is accurate within 4% of the population proportion.

How do you create the dot plot?

​a) Determine the probability of selecting a female.

​(Round to three decimal places as​ needed.)

​b) Determine the probability of selecting a student that is 22 to 24 years old.

​(Round to three decimal places as​ needed.)

​c) Determine the probability of selecting a woman who is 35 years old or older.

​(Round to three decimal places as​ needed.)

​d) Determine the probability of selecting either a student who is a woman or is 25 to 29 years old.

​(Round to three decimal places as​ needed.)

​e) Determine the probability of selecting a​ man, given that the student is 22 to 24 years old.

​(Round to three decimal places as​ needed.)

​f) Determine the probability of selecting a student that is 30 to 34 years​ old, given that the student is a man.

According to a recent​ study, the average length of a newborn baby is 19.219.2 inches with a standard deviation of 1.21.2 inch. The distribution of lengths is approximately Normal. Complete parts​ (a) through​ (c) below. Include a Normal curve for each part.

A.The probability that a baby will have a length of 20.4 inches or more is

B. The probability that a baby will have a length of 21.5 inches or more

C. The probability that a baby will have a length between 17.6 and 20.8 inches

Suppose systolic blood pressure of 16-year-old females is approximately normally distributed with a mean of 119 mmHg and a variance of 398.00 mmHg. If a random sample of 16 girls were selected from the population, find the following probabilities:

a) The mean systolic blood pressure will be below 116 mmHg.

probability = b) The mean systolic blood pressure will be above 123 mmHg.

probability = c) The mean systolic blood pressure will be between 109 and 123 mmHg.

probability = d) The mean systolic blood pressure will be between 105 and 113 mmHg. probability =

A random sample of 172 students was asked to rate on a scale to from 1 (not important) to 5 (extremely important) health benefits as a job characteristic (note that the rating scale can also have decimals, i.e. a student can give a rating of 1.32). The sample mean rating was 3.31, and the sample standard deviation was 0.70. For a type I error of 1% (alpha), can you be reasonably certain that the average rating is more than 3 in the population?

1)Specify the rejection region for  = 0.01. Reject H0 if

A) z > 2.33

B) t > 2.32

C) z < 2.33

D) t < 2.32

and what is your conclusion.

A soft drink filling machine, when in perfect adjustment, fills the bottles with 12 ounces of soft drink. A random sample of 49 bottles is selected, and the contents are measured. The sample yielded a mean content of 11.88 ounces with a standard deviation of 0.35 ounces.

2) State the null and alternative hypotheses.

A) H0: µ = 0, Ha: µ > 11.88

B) H0: µ = 0, Ha: µ ≠ 11.88

C) H0: µ = 0, Ha: µ > 12

D) H0: µ = 0, Ha: µ ≠ 12