A nationwide survey of college students was conducted and found that students spend two hours per class hour studying. A professor at your university wants to determine whether the time students spend at your university is significantly different from the two hours. A random sample of 36 statistics students is carried out and the findings indicate an average of 1.75 hours. Assume a populatoin standard deviation of 0.5 hours. Using a level of significance of 0.05:

1. Construct a 95% confidence interval for the population mean.

2. Using a level of significance of 0.05: a. What is Ho and H1? b. What is the Decision Rule? c. What is the computed value of the test statistic? d. What is the decision regarding Ho? What can we conclude? e. Compute and Interpret the p-value.

3. Are the results from the confidence interval and hypothesis testing consistent? Should they be? Justify your answer.

Cars on Campus. Statistics students at a community college wonder whether the cars belonging to students are, on average, older than the cars belonging to faculty. They select a random sample of 47 cars in the student parking lot and find the average age to be 9.7 years with a standard deviation of 6.5 years. A random sample of 48 cars in the faculty parking lot have an average age of 3 years with a standard deviation of 3.8 years.

Note: The degrees of freedom for this problem is df = 73.845664. Round all results to 4 decimal places. Remember not to round for intermediate calculations!

1. The null hypothesis is ?0:??=??H0:μs=μf. What is the alternate hypothesis?
A. ??:??<??HA:μs<μf
B. ??:??≠??HA:μs≠μf
C. ??:??>??HA:μs>μf

2. Calculate the test statistic.  ? z t X^2 F  =

3. Calculate the p-value for this hypothesis test.  
p value =

4. Suppose that students at a nearby university decide to replicate this test. Using the information from the community college, they calculate an effect size of 1.26. Next, they obtain samples from the university student and faculty lots and, using their new sample data, conduct the same hypothesis test. They calculate a p-value of 0.029 and an effect size of 0.821. Do their results confirm or conflict with the results at the community college?
A. It contradicts the community college results because the effect size is much smaller.
B. It contradicts the community college results because the p-value is much bigger
C. It confirms the community college results because the effect size is nearly the same.
D. It can neither confirm or contradict the community college results because we don't know the sample sizes the university students used.
E. It confirms the community college results because the p-value is much smaller.

Study Guide Chapter 4

Students must be familiar with water as a solvent. Students must be familiar with the characteristics of water as a solvent. Is water the universal solvent? Why or why not? Is the water molecule polar? Why or why not?

Describe the process of hydration.

Define solubility. Do you expect sodium chloride to be soluble in water? Why or why not?   Is ethanol, CH₃CH₂OH, soluble in water? Why or why not? Is hexane, CH₃(CH₂)₄CH₃, soluble in water? Why or why not?

What is a polar bond? Does the water molecule has polar bonds?

Define solute, solvent, strong electrolyte, weak electrolyte and nonelectrolyte. Provide an example of each.

Define strong acids. What is the Arhenius definition of a strong acid? Of the following substances, which are strong acids, if any? CH₃COOH, HCl, CH₃OH, H₂SO₄, and HNO₃.

Define strong bases. Is KOH a strong base? Is NaOH a strong base?

What is a weak acid? Provide an example.

What is a weak base? Provide an example.

Define molarity. What is the use of molarity?

Students must be able to:

Calculate the molarity of a solution given the mass of the solute and the volume of the solution.

Calculate the concentration of ions present in a solution.

Calculate the number of moles of an ion in a solution given the volume of the solution.

Calculate the volume of solution that contains certain mass of solute, given the volume of the solution.

Determine the amount of solid that must be weight in order to prepare a certain volume of solution of a given concentration.

Calculate the volume of a solution of known concentration that is required to prepare a certain volume of a second solution of known concentration.

Calculate the molarity of a solution that is the result of a dilution process.

What is a standard solution? What is a stock solution?

What is dilution? Is it necessary to have a standard solution in order to make a dilution? Is it necessary to have a stock solution in order to make a dilution? Explain your reasoning for both questions.

A useful formula to make a dilution is M₁V₁ = M₂V₂, where M₁ is the molarity of the stock solution, V₁ is the volume of the stock solution, M₂ is the molarity of the desired solution, and V₂ is the volume of the desired solution. Notice that given any 3 quantities on the equation above, we can always solve for the fourth variable. This formula is very useful.

What is a chemical reaction? Define the parts of a chemical equation.

What are precipitation reactions?

What is a precipitate? How do we know when a precipitate is formed?

How do we know if a precipitate forms or not?

Students are expected to understand the solubility rules. Students must be able to apply the solubility rules when predicting the formation of a precipitate.

Students must be able to predict reaction products. How do we predict reactions products?

What is a complete ionic equation? What is the net ionic equation? What is the difference between a complete ionic equation and the net ionic equation?

Students must be able to:

Write formula equations for a given chemical reaction.

Write a complete ionic equation for a given chemical reaction.

Write a net ionic equation for a given chemical reaction.

Students must be able to understand and apply stoichiometry of precipitation reactions.

What is an acid-base reaction? What is an acid? What is a base? What is a neutralization reaction? Provide an example. What are the products of a neutralization reaction?

Students must be able to:

Calculate the volume of an acid of known concentration that is required to neutralize a given volume of base of known concentration.

Calculate stoichiometry for acid-base reactions.

Define acid-base titrations. Provide an example.

What is an indicator? How does an indicator is used in an acid-base reaction? Provide an example.

Define oxidation-reduction reactions. What is a redox reaction? What are the characteristics of these types of reactions? How do we balance oxidation-reduction reactions? Provide an example.

What are oxidation states? Students must be familiar with the rules to calculate oxidation states of an atom.

What is oxidation? What is reduction? How can we identify a specie that is being oxidized and a specie that is been reduced?

Nine students were randomly selected from a population of 1000 students and they were given a math test. Test results are: 95  90   89   85   76 73   92   90  72     What is the 84% confidence interval for the population mean score on the math tests?

a) Do you need any assumptions? If yes, make the assumption.

b) Name the interval

c) 84% CI is

A researcher is interested in heart rates of university students. The researcher randomly selects 52 students from a class they are teaching and measures the students’ heart rates. The data obtained is in the file “Heart Rates.csv”.

1. What is the target population? What is the study population? What is an individual?

2. Is this an observational study or an experiment?

3. The tools you have learned for doing statistical inference require that certain assumptions be met. Check whether these assumptions are satisfied for this dataset.

4. A heart rate of 70 beats per minute (bpm) is considered typical. What type of statistical test is appropriate for this setting? Test the hypothesis that the average heart rate of students in this class is typical. Be sure to include all three steps.

5. Give a 95% confidence interval for the average heart rate of students in the class.

6. Imagine that we know the population standard deviation of heart rates in the class. What type of inference procedure would you use if you had this extra information? How would you expect the margin of error to change?

7. In part 4, you found a statistically significant difference between the mean heart rate of students in the class and a typical heat rate of 70 beats per minute. Based on your answer to part 5, does this difference appear to be practically significant?

Heart Rate Data

To generalize to the weights of all male statistics students or all male college students. Table 1.1 QUANTITATIVE DATA: WEIGHTS (IN POUNDS) OF MALE STATISTICS STUDENTS 160 168 133 170 150 165 158 165 193 169 245 160 152 190 179 157 226 160 170 180 150 156 190 156 157 163 152 158 225 135 165 135 180 172 160 170 145 185 152 205 151 220 166 152 159 156 165 157 190 206 172 175 154

In Chapter 1, Table 1.1 lists the weights of 53 male statistics students.

Although students were asked to report their weights to the nearest pound, inspection of Table 1.1 reveals that a disproportionately large number (27) reported weights ending in either a 0 or a 5. This suggests that many students probably reported their weights rounded to the nearest 5 or 10 pounds rather than to the nearest pound. Using the .05 level of significance, test the null hypothesis that in the underlying population, weights are rounded to the nearest pound. (Hint: If the null hypothesis is true, only two-tenths of all weights should end in either a 0 or a 5, and the remaining eight-tenths of all weights should end in a 1, 2, 3, 4, 6, 7, 8, or 9. Therefore, the situation requires a one-variable test with only two categories, and df = 1.)

Students arrive at a local bar at a mean rate of 30 students per hour. Assume that the bouncer waits X (minutes) to card the next student. That is, X is the time between two students arriving at the bar. Then we know that X has approximately an exponential distribution.

(a) What is the probability that nobody shows up within the 2 minutes after the previous customer?

(b) What is the probability that the next student arrives in the third minute, knowing that nobody has shown up in the 2 minutes since the previous student?

Two separate tests are designed to measure a students ability to solve problems. Several students are randomly selected to take both tests and the results are given below

Test a: 64, 48, 51, 59, 60, 43, 41,42, 35, 50, 45

Test b: 91, 68, 80, 92, 91, 67, 65 ,67, 56, 78, 71

1. FInd the value of the linear correlation coefficient r.

2. Assuming a 0.05 significance level, find the critical value.

3. What do you conclude about the correlation between the two variables.

4. Use the sample data to fine the estimated equation of the regression line.

You are one of the top students in your university’s computer science program of 200 students. You are surprised when you are met after class by two representatives from a federal intelligence agency. Over dinner, they talk to you about the increasing threat of cyberterrorist attacks launched on the United States by foreign countries and the need to counter those attacks. They offer you a position on the agency’s supersecret cyber terrorism unit, at a starting salary 50 percent higher than you know other computer science graduates are being offered. Your role would be to both develop and defend against new zero-day exploits that could be used to plant malware in the software used by the government and military computers. Would such a role be of interest to you? What questions might you ask to determine if you would accept their offer of employment?