A group of researchers is studying the effects of a new diet on cholesterol levels in high-risk patients. The researchers had hypothesized that the cholesterol level would be reduced to a safe level in more than 70% of subjects following the new diet. They are confident that the proportion will be no less than 0.70. To test this one-sided hypothesis, they randomly sampled 200 individuals with dangerously high cholesterol and put them on the new diet. After the period of the study, the researchers determined that 150 of the 200 patients sampled had reduced their cholesterol levels while on the new diet. Find the power of the study. Assume that the significance level is 0.10.

A pharmaceutical company is testing a new drug for a rare disease. In a clinical trial, 1000 patients with the disease were randomly assigned to receive either the new drug or a placebo. After one year, it was found that 60% of the patients who received the new drug experienced improvement, compared to only 40% of those who received the placebo. Is the difference in improvement rates statistically significant? Provide your rationale.

A carnival game is designed so that approximately 10% of players will win a large prize. If there is evidence that the percentage differs significantly from this target, then adjustments will be made to the game. To investigate, a random sample of 100 players is selected from the large population of all players. Of these players, 19 win a large prize. The question of interest is whether the data provide convincing evidence that the true proportion of players who win this game differs from 0.10. Are the conditions for inference met for conducting a z-test for one proportion? Yes, the random, 10%, and large counts conditions are all met. No, the random condition is not met. No, the 10% condition is not met. No, the large counts condition is not met.

In the article “Explaining an Unusual Allergy,” appearing on the Everyday Health Network, Dr. A. Feldweg explained that allergy to sulfites is usually seen in patients with asthma. The typical reaction is a sudden increase in asthma symptoms after eating a food containing sulfites. Studies are performed to estimate the percentage of the nation’s 10 million asthmatics who are allergic to sulfites. In one survey, 38 of 500 randomly selected U.S. asthmatics were found to be allergic to sulfites. Find and interpret a 95% confidence interval for the proportion p of all U.S. asthmatics who are allergic to sulfites.

Sleep apnea is a condition in which the sufferers stop breathing momentarily while they are asleep. This condition results in lack of sleep and extreme fatigue during waking hours. A current estimate is that 18.4 million out of the 312.7 million Americans suffer from sleep apnea, or approximately 5.9 % . A safety commission is concerned about the percentage of commercial truck drivers who suffer from sleep apnea. They do not have any reason to believe that it would be higher or lower than the population's percentage. To test the claim that the percentage of commercial truck drivers who suffer from sleep apnea is not 5.9 % , a simple random sample of 334 commercial truck drivers is examined by a medical expert, who concludes that 11 suffer from sleep apnea. Does this evidence support the claim that the percentage of commercial truck drivers who suffer from sleep apnea is not 5.9 % ? Use a 0.02 level of significance. Step 2 of 3: Compute the value of the test statistic. Round your answer…

Sleep apnea is a condition in which the sufferers stop breathing momentarily while they are asleep. This condition results in lack of sleep and extreme fatigue during waking hours. A current estimate is that 16.3 million out of the 312.7 million Americans suffer from sleep apnea, or approximately 5.2%. A safety commission is concerned about the percentage of commercial truck drivers who suffer from sleep apnea. They do not have any reason to believe that it would be higher or lower than the population’s percentage. To test the claim that the percentage of commercial truck drivers who suffer from sleep apnea is not 5.2%, a simple random sample of 380380 commercial truck drivers is examined by a medical expert, who concludes that 29 suffer from sleep apnea. Does this evidence support the claim that the percentage of commercial truck drivers who suffer from sleep apnea is not 5.2%? Use a 0.01 level of significance.   Step 1 of 3 :  State the null and alternative hypotheses for the test.…

A scientist is studying the effect of a new type of exercise program on cardiovascular health. The scientist randomly assigns individuals to either the exercise program or a control group. The scientist wants to determine if the exercise program has a statistically significant effect on cardiovascular health. The scientist monitors cardiovascular health by measuring the blood pressure of each individual.

Sleep apnea is a condition in which the sufferers stop breathing momentarily while they are asleep. This condition results in lack of sleep and extreme fatigue during waking hours. A current estimate is that 12.8 million out of the 312.7 million Americans suffer from sleep apnea, or approximately 4.1%. A safety commission is concerned about the percentage of commercial truck drivers who suffer from sleep apnea. They do not have any reason to believe that it would be higher or lower than the population’s percentage. To test the claim that the percentage of commercial truck drivers who suffer from sleep apnea is not 4.1%, a simple random sample of 392 commercial truck drivers is examined by a medical expert, who concludes that 2424 suffer from sleep apnea. Does this evidence support the claim that the percentage of commercial truck drivers who suffer from sleep apnea is not 4.1%? Use a 0.02 level of significance.   Step 3 of 3 : Draw a conclusion and interpret the decision.   1.…

Sleep apnea is a condition in which the sufferers stop breathing momentarily while they are asleep. This condition results in lack of sleep and extreme fatigue during waking hours. A current estimate is that 12.8 million out of the 312.7 million Americans suffer from sleep apnea, or approximately 4.1%. A safety commission is concerned about the percentage of commercial truck drivers who suffer from sleep apnea. They do not have any reason to believe that it would be higher or lower than the population’s percentage. To test the claim that the percentage of commercial truck drivers who suffer from sleep apnea is not 4.1%, a simple random sample of 392 commercial truck drivers is examined by a medical expert, who concludes that 24suffer from sleep apnea. Does this evidence support the claim that the percentage of commercial truck drivers who suffer from sleep apnea is not 4.1%? Use a 0.02 level of significance.   Step 2 of 3: Compute the value of the test statistic. Round your…

Sleep apnea is a condition in which the sufferers stop breathing momentarily while they are asleep. This condition results in lack of sleep and extreme fatigue during waking hours. A current estimate is that 10.9 million out of the 312.7 million Americans suffer from sleep apnea, or approximately 3.5 % . A safety commission is concerned about the percentage of commercial truck drivers who suffer from sleep apnea. They do not have any reason to believe that it would be higher or lower than the population's percentage. To test the claim that the percentage of commercial truck drivers who suffer from sleep apnea is not 3.5 % , a simple random sample of 308 commercial truck drivers is examined by a medical expert, who concludes that 19 suffer from sleep apnea. Does this evidence support the claim that the percentage of commercial truck drivers who suffer from sleep apnea is not 3.5 % ? Use a 0.05 level of significance. Step 1 of 3: State the null and alternative hypotheses for the test.…