A claim was made by your professor that the second exam in the class had an average score of 73. By speaking with fellow students, you think this value is probably higher than the true class average. Logically, the highest score in the exam was probably very high, so you estimate the max score to be a 100%. The lowest score you can imagine anyone getting is a 30% (this is just a guess). Approximately how many people should you plan to survey if you want an estimate of the true mean within 2% of the true value with 90% confidence?
Consider a situation where we are looking at the dissolved oxygen content of surface water through the month of April. For a healthy aquatic system, DO should be at 11 mg per L. After sampling every day of the month (30 observations), the mean DO was at 10.6 mg/L. The population standard deviation on DO in April is 1.2 mg/L. Is there evidence of low dissolved oxygen content at the 95% level of confidence?
a.) Set up the Null and Alternative Hypothesis
b.) Which is the appropriate test for this data?
c.) What is the value of the standardized test statistic?
d.) What is the p-value associated with this test statistic?
e.) What can you conclude about whether or not the dissolved oxygen content is low or not?
f.) Could you have committed a type 1 or type 2 error here?
At a grocery store, based on sampling 100 customers, you conclude that the average monthly expenditures by each customer on your products during the next month will be at an estimated $212. The true standard deviation of expenditures is $112.
a.) Obtain a 90% confidence interval for the average expenditure estimate.
b.) Interpret this confidence interval.
The production of potatoes requires a significant use of water. On average, 1 kg of potatoes requires 287 L of water to produce. Suppose that a new method is advertized to produce potatoes that claims to require 10% less water. You carefully utilize this method on 10 separate plots producing 1 kg per plot. The average production on these plots requires 269 L of water with a sample standard deviation of 20 L of water. Is there evidence to suggest that the advertized water rate is false at the 96% level of confidence?
a.) Set up the Null and Alternative Hypothesis
b.) Which is the appropriate test for this data?
c.) What is the value of the standardized test statistic?
d.) What is the p-value associated with this test statistic?
e.) What can you conclude about whether the claim is false or not?
f.) Could you have committed a type 1 or type 2 error here?
g.) Create a 92% Confidence interval around the estimated mean.
Two machines are producing "identical" aluminum tubes that that are supposed to have length 150mm. The machinist takes a sample of 17 parts from machine 1 and finds the average length to be 148.2mm and standard deviation of 6mm. The sample of 19 parts taken from machine 2 had a mean of 151.5mm and standard deviation of 4mm. With 95% confidence, are the machines producing parts of the same length?
a.) What is the appropriate test for this question?
b.) Set up the null and alternative hypothesis.
c.) What is the test statistic for this test?
d.) What are the degrees of freedom for this test?
e.) What is the p-value for this test?
f.) Based on this p-value, what can you infer about the original question?
g.) Form and interpret 95% confidence interval around the estimated difference.
Sixteen people volunteered to be part of an experiment. All 16 people were Caucasian, between the ages of 25 and 35, and were supplied with nice clothes. Eight of the people were male and eight were female. The question of interest in this experiment was whether females received faster service at restaurants than males. Each of the eight male participants were randomly assigned a restaurant, and each of the eight females was randomly assigned to one of these same restaurants. One Friday night, all 16 people went out to eat, each one alone. The male and female assigned to the same restaurant would arrive within 5 minutes of each other, with the order determined by flipping a coin. Each person then ordered a similar drink and similar meal. The time (in minutes) until the food arrived at the table was recorded. These are below.
Restaurant 1 2 3 4 5 6 7 8
Male 22 14 16 26 18 13 9 27
Female 25 12 13 21 21 14 9 16
a.) What is the appropriate test to use for this data?
b.) Set up the null and alternative hypothesis
c.) Calculate the test statistic.
d.) Determine the degrees of freedom for this problem.
e.) Complete this test for the question at 95% level of confidence
f.) What assumptions must be made for this test to work?
A super-majority of students (70% for this case) are needed to pass a referendum on tuition increases for a large university with over 70,000 students. How many students should be sampled in order to have an estimate of the true proportion of students that support the referendum that is within 3% of the true proportion with 96% confidence?
In the situation above, only 600 people responded to the survey of students that was sent. Out of this sample, 442 responded positively to the questionnaire. Is there evidence at the 96% level of confidence that more than 70% of the student body will support the proposal?
a.) What test should be used to answer this question?
b.) Set up the null and alternative hypothesis
c.) What is the value of the standardized test statistic for this problem?
d.) What is the p-value associated with this test?
e.) What conclusion can you reach from this p-value?
f.) Produce a 92% confidence interval surrounding your estimated proportion.
A claim is made that a daily vitamin C dose will help you avoid getting the flu. In order to test this claim, two groups of people are randomly selected, one a control group of 75 people and the other a treatment group of 93 people. In the control group, 43 people were diagnosed with the flu during that season. In the treatment group, 46 got the flu. Is there evidence at the 90% level of confidence to suggest that the vitamin C dose is effective?
a.) What test should be used to answer this question?
b.) Set up the null and alternative hypothesis
c.) Find the value of the test statistic associated with this test.
d.) Determine the p-value for this test
e.) State the conclusion for this test.
1.) The correlation coefficient between age and GAG is -0.705266. What does this mean in terms of the direction and strength of the association between these variables?
2.) What is the coefficient of determination here and what does it mean?
3.) Identify the explanatory and response variables in this model.
4.) What are the intercept and slope coefficients and what do they mean?
5.) Is age a statistically significant predictor of GAG in this model?
6.) For a child of age 5, what is the expected value of GAG?
7.) An observation of a 5 year old in this data yields a value of 7.82 What is the residual for this observation?