A computer manufacturing company claims that only 7.5% of their computers are returned. Kelly thinks that the company is misrepresenting the true proportion of computers that are returned, and that the true proportion is higher than they claim. She wants to test this using α = 0.01. Kelly takes a sample of 220 computers and observes that 25 are returned. Assume a normal sampling distribution. (a) What are the null and alternative hypotheses? H0: HA: (b) What is the test statistic? (Round your answer to 2 decimal places, if needed.) (c) Using the statistical table, what is the p-value? (Round your answer to 4 decimal places, if needed.)
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A computer manufacturing company claims that only 7.5% of their computers are returned. Kelly thinks that the company is misrepresenting the true proportion of computers that are returned, and that the true proportion is higher than they claim. She wants to test this using α = 0.01. Kelly takes a sample of 220 computers and observes that 25 are returned. Assume a normal sampling distribution.
(a) What are the null and alternative hypotheses?
H0:
HA:
(b) What is the test statistic? (Round your answer to 2 decimal places, if needed.)
(c) Using the statistical table, what is the p-value? (Round your answer to 4 decimal places, if needed.)
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- 8- A random sample of the weight of 8 newborn babies at a local hospital is 6.5, 9.2, 8.5, 7.5, 6.7, 7.4, 8.2, and 7.1. Conduct a test of hypothesis to determine if the population mean is 7 pounds. (15%) b. Construct a 95% confidence interval for population standard deviation (6). Test if population variance (o) of the weight of newborns is equal to 0.25. Use a-0.10 and make sure to identify the null and the alternative, the test statistics, critical value(s), and the decision rule. d. What assumptions are needed for the validity of your answers in parts a, b, and c? a. с.For the population of people in the United States who are at least 18 years of age, approximately 61 percent voted in a recent election. A random sample of 200 people and a random sample of 100 people will be selected from the population. For which sample size is it more likely that greater than 70 percent of the sample voted in the recent election? (A) They are equally likely, because the mean of the sampling distribution is the same for both sample sizes. It is more likely for a sample size of 200 people, because there is more variability in the sampling distribution for larger sample sizes. (B) (D) It is more likely for a sample size of 200 people, because there is less variability in the sampling distribution for larger sample sizes. It is more likely for a sample of size 100 people, because there is more variability in the sampling distribution for smaller sample sizes. It is more likely for a sample size of 100 people, because there is less variability in the sampling…We have Ho : p = .4 and H1: p > .4. You run 50 experiments and find that the sample proportion is .42. Use alpha = .01 to test the hypothesis.
- You have an independent-measures study where your first sample has an s² = 9 and your second sample has an s? = 6. a. If your sample size for both samples is n= 5, find the sample variances and compute the pooled variance. b. On the other hand, if your samples have difference sample sizes, n1 = 5 and n2 13. Again, calculate the two sample variances and your pooled variance, c. Compare your answers from part a and b. Why are there differences?A manufacturer claims that only 2% of their products are defective. A store receives a delivery of 300 items from the manufacturer. Let p-hat = the proportion of defective items in a sample of 300 items. Assuming the manufacturer is correct that only 2% of their products are defective, what are the mean and standard deviation of the sampling distribution of p-hat ? Options: The mean is 0.02 and the standard deviation is 0.008. The mean is 6 and the standard deviation is 2.42. The mean is 6 and the standard deviation is 5.88. The mean is 0.02 and the standard deviation is 0.196.It is believed that 70% of males pass their drivers test in the first attempt, while 65% of females pass the test in the first attempt. A test will be conducted to check whether the proportions are in fact equal. a. State the hypotheses in terms of the appropriate parameter(s)b. Determine if the samples are independent or dependentc. Identify the random variable, and its distribution (either normal or t-distribution), along and explain this choice. d. Identify the test to be used.
- You are interested in testing whether the average age of household heads is higher in the suburbs than in inner city neighbourhoods. A survey is conducted, and the following results are obtained. In the suburbs, the household heads of the 45 households surveyed had a mean age of 44 with a standard deviation of 15. In the inner city, the mean age of the 40 household heads surveyed was 38 with a standard deviation of 13. Assuming that the populations from which these samples were drawn have equal variances, can you conclude that the difference between the two means is significant at the 95% level of confidence? (a) Write in words and symbols the null and research hypotheses. (b) Assuming the variances of the populations are equal, calculate the value of the Pooled Variance Estimate (PVE). (c) Calculate the value of the standard error for the difference between the two means.A researcher studying public opinion of proposed Social Security changes obtains a simple random sample of 25 adult Americans and asks them whether or not support the proposed changes . To say that the distribution of the sample proportion of adults who respond yes, is approximately normal , how many more adult Americans does the researcher need to sample in the following cases? (a) 15% of all adult Americans support the changes (b) 20% of all adult Americans support the changesIn a survey of 175 females who recently completed high school, 76% were enrolled in college. In a survey of 150 males who recently completed high school, 72% were enrolled in college. At a = 0.05, can you reject the claim that there is no difference in the proportion of college enrollees between the two groups? Assume the random samples are independent. Complete parts (a) through (e). O A. Ho: P1 #P2 Ha: P1 = P2 O B. Ho: P1 P2 OF. Ho: P1 = P2 O D. Ho: P1 > P2 Ha: P1 SP2 Ha: P1 O B. z 1.96 O D.In case of hypothesis testing in places where population variances are unknown and sample size is large (nl and n22 30), sample variances can be a good approximation of population variances. Which best describe this statement? Select one: O a. None of the choices O b. The statement is true c. The statement is false O d. Not enough data to support the statement O e. The statement is neither true nor falseIn a particular year, registered nurses earned an average annual salary of $52,330. A survey was conducted with 48 nurses from a particular state to determine if the annual salary is higher than $52,330 for that state's nurses. The sample average was $61,599 with a sample standard deviation of $7,489. Conduct a hypothesis test at the 5% level.Note: If you are using a Student's t-distribution for the problem, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.) State the distribution to use for the test. (Enter your answer in the form z or tdf where df is the degrees of freedom.) What is the test statistic? (Round your answer to two decimal places.) What is the p-value? (Round your answer to four decimal places.) Construct a 95% confidence interval for the true mean. Sketch the graph of the situation. Label the point estimate and the lower and upper bounds of the confidence interval. (Round your answers to the…Determine whether carpeted rooms have more bacteria than uncarpeted rooms at the a = 0.05 level of significance. Normal probability plots indicate that the data are approximately normal and boxplots indicate that there are no outliers. State the null and alternative hypotheses. Let population 1 be carpeted rooms and population 2 be uncarpeted rooms. A. Ho: H1= H2 H1: H1> H2 B. Ho: H1 H2 c. 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