Hypothesis Testing Examples, Exams of Nursing

Download Hypothesis Testing Examples and more Exams Nursing in PDF only on Docsity! Week 7 Assignment Hypothesis Test for the Mean - Population Standard Deviation Known Question Jamie, a bowler, claims that her bowling score is less than 168 points, on average. Several of her teammates do not believe her, so she decides to do a hypothesis test, at a 1% significance level, to persuade them. She bowls 17 games. The mean score of the sample games is 155 points. Jamie knows from experience that the standard deviation for her bowling score is 19 points.  H0: μ≥168; Ha: μ<168  α=0.01 (significance level) What is the test statistic (z-score) of this one-mean hypothesis test, rounded to two decimal places? Question A politician claims that at least 68% of voters support a decrease in taxes. A group of researchers are trying to show that this is not the case. Identify the researchers' null hypothesis, H0, and the alternative hypothesis, Ha, in terms of the parameter p. Question Annie, a long jumper, claims that her jump distance is not equal to 19 feet, on average. Several of her teammates do not believe her, so she decides to do a hypothesis test, at a 10% significance level, to persuade them. She makes 24 jumps. The mean distance of the sample jumps is 19.5 feet. Annie knows from experience that the standard deviation for her jump distance is 1.2 feet.  H0: μ=19; Ha: μ≠19  α=0.1 (significance level) What is the test statistic (z-score) of this one-mean hypothesis test, rounded to two decimal places? Question Determine the Type II error if the null hypothesis, H0, is: a wooden ladder can withstand weights of 250 pounds and less. Answer Explanation Correct answer: You think the ladder can withstand weight of 250 pounds and less when, in fact, it cannot. A Type II error is the decision not to reject the null hypothesis when, in fact, it is false. In this case, the Type II error is thinking the ladder can withstand weights of 250 pounds and less when, in fact, it cannot. Question Suppose the null hypothesis, H0, is: the mean age of the horses on a ranch is 6 years. What is the Type II error in this scenario? Correct answer: You think the mean age of the horses on a ranch is 6 years when, in fact, it is not. A Type II error is the decision not to reject the null hypothesis when, in fact, it is false. In this case, the Type II error is thinking that the mean age of the horses is 6 years when, in fact, it is not. Question Find the graph that matches the following hypothesis test. H0:X≥6.4, Ha:X<6.4 Correct answer: A normal curve is over a horizontal axis and is centered on 6.4. A tick is labeled on a point to the left of 6.4. The area under the curve and to the left of the tick is shaded. The alternative hypothesis, Ha, tells us which area of the graph we are interested in. Because the alternative hypothesis is X<6.4, we are interested in the region less than (to the left of) 6.4, so the correct graph is the first answer choice. Question Which graph below corresponds to the following hypothesis test? H0:p≤8.1, Ha:p>8.1 Correct answer: The researchers conclude that the rack holds less than 100 pounds of force, but the rack actually holds more than 100 pounds. Remember that a Type I error is rejecting the null hypothesis when the null hypothesis is true and a Type II error is not rejecting the null hypothesis when it is false. We are asked for the Type I error in this scenario. Rejecting the null hypothesis means rejecting the statement that the rack can hold more than 100 pounds. Therefore, a Type I error is: The researchers conclude that the rack holds less than 100 pounds when in reality it holds at least 100 pounds. Question Determine the Type I error if the null hypothesis, H0, is: the percentage of homes in the city that are not up to the current electric codes is no more than 10%. And, the alternative hypothesis, Ha, is: the percentage of homes in the city that are not up to the current electric codes is more than 10%. Correct answer: There is sufficient evidence to conclude that more than 10% of homes in the city are not up to the current electrical codes when, in fact, there are no more than 10% that are not up to the current electric codes. A Type I error is the decision to reject the null hypothesis when it is true. In this case, the Type I error is when there is sufficient evidence to conclude that more than 10% of homes in the city are not up to the current electrical codes when, in fact, there are no more than 10% not up to the current electric codes. Question Determine the Type I error if the null hypothesis, H0, is: a wooden ladder can withstand weights of 250 pounds and less. Correct answer: You think the ladder cannot withstand weight of 250 pounds and less when, in fact, it really can. A Type I error is the decision to reject the null hypothesis when it is true. In this case, the Type I error is thinking the wooden ladder cannot withstand the weights of 250 pounds or less when it really can. Question Which of the following results in a null hypothesis p≤0.47 and alternative hypothesis p>0.47? Correct answer: An online article claims that at most 47% of internet users participate in social media. A group of researchers think this is incorrect, and they want to show that more than 47% of internet users participate in social media. Remember that the null hypothesis is the statement that the researchers are trying to reject, or show is wrong. In this case, the null hypothesis is p≤0.47, which should be what the online article claims. The alternative hypothesis, p>0.47, should be what the researchers are trying to show. So the fourth answer choice is correct. Question A car magazine claims that 68% of car owners follow a normal maintenance schedule. A mechanic does not think this is accurate, and so he wants to show that the percentage of people who follow a normal maintenance schedule is not equal to 68%. Identify the null hypothesis, H0, and the alternative hypothesis, Ha, in terms of the parameter p. Correct answer: H0: p=0.68; Ha: p≠0.68 The null hypothesis is the stated or claimed fact that the researcher is trying to refute or reject. In this case, this is the claim of the car magazine that 68% of car owners follow a normal maintenance schedule. So H0 is p=0.68. The alternative hypothesis Ha is what the researcher (the mechanic in this case) is trying to show. It is the opposite of the null hypothesis. Namely, Ha is p≠0.68. Question Which of the following answers give valid null and alternative hypotheses for a hypothesis test? Select all correct answers. Correct answer: H0: μ≥15; Ha: μ<15 H0: μ=15; Ha: μ≠15 Remember that the null hypothesis H0 includes equality as part of the relationship, so the valid hypothesis tests above are  H0: μ≥15; Ha: μ<15  H0: μ=15; Ha: μ≠15 Question A mattress store advertises that their beds last at least 5 years, on average. A consumer group thinks that they do not last that long and wants to set up a hypothesis test. If μ denotes the average time, in years, that the mattresses last, what are the null and alternative hypotheses in this situation? Correct answer: H0: μ≥5; Ha: μ<5 Lexie, a bowler, claims that her bowling score is more than 140 points, on average. Several of her teammates do not believe her, so she decides to do a hypothesis test, at a 5% significance level, to persuade them. She bowls 18 games. The mean score of the sample games is 155 points. Lexie knows from experience that the standard deviation for her bowling score is 17 points.  H0: μ≤140; Ha: μ>140  α=0.05 (significance level) What is the test statistic (z-score) of this one-mean hypothesis test, rounded to two decimal places? Correct answers:  Test statistic = 3 point 7 4 $\text{Test statistic = }3.74$  The hypotheses were chosen, and the significance level was decided on, so the next step in hypothesis testing is to compute the test statistic. In this scenario, the sample mean score, x¯=155. The sample the bowler uses is 18 games, so n=18. She knows the standard deviation of the games, σ=17. Lastly, the bowler is comparing the population mean score to 140 points. So, this value (found in the null and alternative hypotheses) is μ0. Now we will substitute the values into the formula to compute the test statistic: z0=x¯−μ0σn√=155−1401718√≈154.007≈3.74 So, the test statistic for this hypothesis test is z0=3.74. Question Suppose a pitcher claims that her pitch speed is not equal to 45 miles per hour, on average. Several of her teammates do not believe her, so the pitcher decides to do a hypothesis test, at a 1% significance level, to persuade them. She throws 21 pitches. The mean speed of the sample pitches is 46 miles per hour. The pitcher knows from experience that the standard deviation for her pitch speed is 6 miles per hour.  H0: μ=45; Ha: μ≠45  α=0.01 (significance level) What is the test statistic (z-score) of this one-mean hypothesis test, rounded to two decimal places? Question Suppose the null hypothesis, H0, is: doctors believe that a surgical procedure is successful at least 80% of the time. Which of the following gives β, the probability of a Type II error? Correct answer: the probability that doctors think the surgical procedure is successful at least 80% of the time when, in fact, it is not A Type II error is the decision not to reject the null hypothesis when, in fact, it is false. In this case, the Type II error is when the doctors think that the surgical procedure is successful at least 80% of the time when, in fact, it is not. Question What is α, the probability of a Type I error if the null hypothesis, H0, is: Carmin believes that her chemistry exam will only cover material from chapters four and five. Correct answer: the probability that Carmin believes that her chemistry exam will not cover material only from chapters four and five when, in fact, it will only cover material from chapters four and five A Type I error is the decision to reject the null hypothesis when it is true. In this case, the Type I error is when Carmin believes that her chemistry exam will not cover only material from chapters four and five when, in reality, it will. Question Suppose the null hypothesis, H0, is: a sporting goods store claims that at least 70% of its customers do not shop at any other sporting goods stores. What is the Type I error in this scenario? Correct answer: The sporting goods store thinks that less than 70% of its customers do not shop at any other sporting goods stores when, in fact, at least 70% of its customers do not shop at any other sporting goods stores. A Type I error is the decision to reject the null hypothesis when it is true. In this case, the Type I error is when the store thinks that less than 70% of its customers only shop at their sporting goods store when, in fact, it is at least 70%. Question Determine the Type II error if the null hypothesis, H0, is: researchers claim that 65% of college students will graduate with debt. Correct answer: The researchers think that 65% of college students will graduate with debt when, in fact, more or less than 65% of college students will graduate with debt. A Type II error is the decision not to reject the null hypothesis when, in fact, it is false. In this case, the Type II error is when the researchers think that 65% of college students will graduate with debt when, in fact, more or less than 65% will graduate with debt.