For questions 1-5, write the null and alternative hypothesis.
1. Does the water temperature have an effect on the number of people in the pool?
2. Does the weather have an effect on the number of people at the beach?
3. A fitness center is running a discounted membership fee. Did the discount increase the membership sales? Write your hypotheses mathematically.
4. A medical researcher gave 100 patients a new drug to see if it reduces their blood pressure? Did the new drug reduce the patients' blood pressure? Write your hypothesis mathematically.
5. Some students took a conflict resolution class? Did this class help to reduce the number of conflicts that the students were involved in? Write your hypothesis mathematically.
For questions 6-10, find the critical value.
6. There is an annual hot dog eating contest in Plattsburg, MS and the average number of hot dogs eaten by one person is 36 with a standard deviation of 6. Find the critical value for a person who can eat more than 2 deviations above the mean.
7. Female high school seniors at a particular school have an average height of 65 inches with a standard deviation of 5 inches. Find the critical value for a female high senior who is less than 1 deviation from the mean.
8. The average weight of a newborn at a particular hospital is 96 ounces with a standard deviation of 3 ounces. Find the critical value for a newborn who is 2 standard deviations below the average weight.
9. A company found that 27 out of 150 of its products were defective after retraining its employees. If the company normally has a 40% defective product rate, find the critical value to determine if retraining the employees helped to minimize the number of defective products.
10. A teacher gives 200 students a study guide for a test and the average score was 90 with a standard deviation of 6. She did not give the other 200 students a study guide and their average score was 70 with a standard deviation of 8. Find the critical value to determine whether or not the study guide helped students to increase their test score.
Ho: water has no effect
H1: water has effect
Ho: Weather has no effect ...
H1: Weather does...
1. Null hypothesis: Water temperature does not have an effect on the number of people in the pool.
Alternative hypothesis: Water temperature has an effect on the number of people in the pool.
2. Null hypothesis: Weather does not have an effect on the number of people at the beach.
Alternative hypothesis: Weather has an effect on the number of people at the beach.
3. Null hypothesis: The discount did not increase the membership sales. (H0: μ0)
Alternative hypothesis: The discount increased the membership sales. (HA: μ > μ0)
4. Null hypothesis: The new drug did not reduce the patients' blood pressure. (H0: μ0)
Alternative hypothesis: The new drug reduced the patients' blood pressure. (HA: μ < μ0)
5. Null hypothesis: The conflict resolution class did not help reduce the number of conflicts that the students were involved in.
Alternative hypothesis: The conflict resolution class helped to reduce the number of conflicts that the students were involved in.
6. To find the critical value, we need to determine the area in the right tail for a standard normal distribution. Since we want to find the critical value at more than 2 standard deviations above the mean (assuming a two-tailed test), we are looking for the area in the right tail corresponding to a z-score of 2. To find this, we can use a standard normal distribution table or a statistical calculator to find the corresponding critical value, which is approximately 2.05.
7. To find the critical value, we need to determine the area in the left tail for a normal distribution. Since we want to find the critical value at less than 1 standard deviation from the mean (assuming a two-tailed test), we are looking for the area in the left tail corresponding to a z-score of -1. To find this, we can use a standard normal distribution table or a statistical calculator to find the corresponding critical value, which is approximately -1.645.
8. To find the critical value, we need to determine the area in the left tail for a normal distribution. Since we want to find the critical value at more than 2 standard deviations below the mean (assuming a two-tailed test), we are looking for the area in the left tail corresponding to a z-score of -2. To find this, we can use a standard normal distribution table or a statistical calculator to find the corresponding critical value, which is approximately -2.05.
9. To determine if retraining the employees helped minimize the number of defective products, we can use a hypothesis test for proportions. The critical value can be found using a Z-table or calculator based on the significance level (alpha) and the degrees of freedom. In this case, the degrees of freedom would be n - 1, where n is the sample size (150). The critical value would be the Z-value corresponding to the desired significance level (e.g., 0.05 or 0.01) for a one-tailed test.
10. To determine if the study guide helped students increase their test score, we can use a hypothesis test for the difference in means. The critical value can be found using a t-table or calculator based on the degrees of freedom and the significance level (alpha). The degrees of freedom would be (n1 - 1) + (n2 - 1), where n1 and n2 are the sample sizes (200 each). The critical value would be the t-value corresponding to the desired significance level (e.g., 0.05 or 0.01) for a two-tailed test.
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6. Z = (score-mean)/SD = +2
Solve for score/critical value.