Calculations
Calculate the critical value (z) for a left tailed test when alpha=.04
What is -1.75
In a null hypothesis, the sign of the statement is always________.
The null hypothesis is detonated with_______.
=
Ho
Studies indicate that about 10 percent of polar bears weigh more than 1,000 pounds. A biologist studying the bears thinks that percent might be too high. From a random sample of polar bears, the biologist found only 8 percent of the sample weighing over 1,000 pounds. Which type of test would be the most appropriate method for the biologist’s to use?
a one sample z test for the population proportion using the sample proportion.
The probability of obtaining a sample statistic as extreme as the one obtained if the null hypothesis is assumed to be true is the ______.
P-Value
What gives the probability of making a Type I error?
significance level
For a certain brand of canned corn, the company claims that the mean weight of the contents of the cans is 15.25 ounces. A random sample of 36 cans were selected. The sample was found to have mean 15.18 ounces and standard deviation 0.12 ounce. A hypothesis test will be conducted to investigate whether there is evidence to support the belief that the mean is less than 15.25 ounces.
What is the test statistic for the hypothesis test?
What is t stat = -3.5
Hypotheses are always about the _________, never about the sample.
population
For a one-sample test for a population proportion p and sample size n, why is it necessary that np>10 and n(1−p)>10 ?
The sample size must be large enough to support an assumption that the sampling distribution of the sample proportion is approximately normal.
A magazine article reported that college students spend an average of $100 on a first date. A university sociologist believed that number was too high for the students at the university. The sociologist surveyed 32 randomly selected students from the university and obtained a sample mean of $92.23 for the most recent first dates. A one-sample t-test resulted in a p-value of 0.026.
Interpret the P-Value
If the mean amount of money that students from the university spend on a first date is $100, the probability is 0.026 that a randomly selected group of 32 students from the university would spend a mean of $92.23 or less on their most recent first dates.
Consider the results of a hypothesis test; which indicate there is not enough evidence to reject the null hypothesis. Which type of error could be made?
A type 2 error but not type 1.
Find the critical value (z) for a two tailed test when alpha=0.02
What is plus or minus 2.33
Hypothesis tests are designed to measure the _________ of evidence against the null hypothesis.
We never _______ a null hypothesis; we either do or do not have evidence to reject it.
The alternative hypothesis is ___________ if there is interest in deviations from the null hypothesis in only one direction.
Strength
Accept
One- Sided
The distribution of mass for United States pennies minted since 1982 is approximately normal with mean 2.5 grams. A random sample of 10 pennies minted since 1982 was selected. The sample had a mean mass of 2.47 grams and a standard deviation of 0.04 gram.
The test statistic for the population mean has which of the following distributions?
A t-distribution with 9 degrees of freedom.
The plant manager of a company that makes pillows claims that only 8 percent of the pillows made have a stitching defect. The quality control director thought that the percent might be different from 8 percent and selected a random sample of pillows to test. The director tested the hypotheses H0:p=0.08 versus Ha:p≠0.08 at the significance level of α=0.05. The p-value of the test was 0.03. Assuming all conditions for inference were met, what is the correct conclusion?
The p-value is less than α, and the null hypothesis is rejected. There is convincing evidence to suggest the true proportion of stitching defects is not 0.08.
A school superintendent must make a decision whether or not to cancel school because of a threatening snow storm.
What would the results be of Type I and Type II errors for the null hypothesis: The weather remains dry.
Type I: Weather remains dry, school is needlessly canceled.
Type II: School isn't canceled and the storm hits.
A study found that the average stopping distance of a school bus traveling 50 miles per hour was 264 feet. A group of automotive engineers decided to conduct a study of its school buses and found that for 31 buses, the average stopping distance of buses traveling 50 miles per hour was 262.3 feet and the standard deviation was 3 feet. Test the claim that the average stopping distance of the company’s buses is actually less than 264 feet. Find the P-value. On the basis of the P-value, should the null hypothesis be rejected at a =0.01?
What is reject null. p=.0018
The germination rate is the rate at which plants begin to grow after the seed is planted. A seed company claims that the germination rate for their seeds is 90 percent. Concerned that the germination rate is actually less than 90 percent, a botanist obtained a random sample of seeds, of which only 80 percent germinated. What are the correct hypotheses for a one-sample z-test for a population proportion p ?
Ho: P=0.90
Ha: P<0.90
How do we check for independent selections?
Why do we need to do this for a hypothesis test?
N> 10n
We use a hypothesized sampling distribution to calculate our p-values.
The independent sections check allows us to use the "short formulas" for stand. deviation for a sampling distribution.
A significance test is conducted for which the alternative hypothesis states that more than 83 percent of all adult sea turtles on a certain beach are female. A random sample of adult sea turtles from the beach found that 85 percent of the sea turtles were female. The p-value for the test is 0.408. If the null hypothesis is true, interpret the p-value?
Of all possible samples of the same size, 40.58 percent will result in 85 percent or more of adult sea turtles on the beach being female.
Machines at a bottling plant are set to fill bottles to 12 ounces. The quality control officer at the plant periodically tests the machines to be sure that the bottles are filled to an appropriate amount. The null hypothesis of the test is that the mean is at least 12 ounces. The alternative hypothesis is that the mean is less than 12 ounces. Describe a Type One Error.
The test provides convincing evidence that the mean is less than 12 ounces, but the actual mean is at least 12 ounces.
For a certain year a study reports that the percentage of college students using credit cards was 83%. A college dean of student services feels that this is too high for her university, so she randomly selects 50 students and finds that 40 of them use credit cards. At a alpha=? 0.04, is she correct about her university?
What is do not reject null. z=-.565
Ms. Lagimoniere was bored and researched endangered animals. She claims the average number of snow leopards born a year is 50. You think she is incompetent on this matter. Write the null and alternative hypothesis.
Ho: mean of pop = 50
Ha: mean of pop is not 50
Make up a problem that would require us to use a hypothesis test.
Be creative.
Most dermatologists recommend that the ideal shower lasts approximately 10 minutes. A researcher suspects that the average shower length of high school students is greater than 10 minutes. To test the belief, the researcher surveyed 125 randomly selected high school students and found that their average shower length was 14.7 minutes. With all conditions for inference met, a hypothesis test was conducted at the significance level of α=0.05, and the test produced a p-value of 0.0000.
What can you conclude?
The researcher has statistical evidence to conclude that the population mean shower length for high school students is greater than 10 minutes.
Medical researchers are testing a new surgical procedure designed to minimize the side effects of surgery. The null hypothesis is that the procedure is not effective in minimizing side effects. For the researchers, the more consequential error would be that the procedure actually is effective in minimizing the side effects, but the test does not detect the effectiveness of the procedure.
We would want to increase the probability of what kind of error?
Type 1 Error