Carpetland carpet installers earn an average profit of $300 for each carpet installed. Joan Chen, the firm's vice president, proposes a new procedure for installations, which she hopes will be more efficient. Joan hopes that the results of a trial period will enable her to conclude with a level of significance of 0.05 that the new procedure increases the average profit of installing a carpet. What will be the consequences if she makes a Type I error on her hypothesis test?
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- A randomized experiment was performed to determine whether two fertilizers, A and B, give different yields of tomatoes. A total of 33 tomato plants were grown; 14 using fertilizer A and 19 using fertilizer B. The distributions of the data did not show marked skewness and there were no outliers in either data set. The results are below. Is there evidence of a significant difference between the tomato yields based on the fertilizer brand? Fertilizer Fertilizer B Average number of tomatoes per plant 18.4 19.1 Standard deviation 3.2 4.7 Number of plants 19 14A statistics teacher taught a large introductory statistics class, with 500 students having enrolled over many years. The mean score over all those students on the first midterm was µ = 78 with standard deviation o = 10. One year, the teacher taught a much smaller class of only 25 students. The teacher wanted to know if teaching a smaller class was more effective and students performed better. We can consider the small class as an SRS of the students who took the large class over the years. The average midterm score was ī = 83. The hypothesis should be: Но : и 3D 78 vs. Ha : и > 78. O Ho : µ = 78 vs. Ha : µ = 88. Ho : µ = 88 vs. H. : µ < 88. Но : и 3D 88 vs. Ha : и 3D 78.Researchers wish to investigate whether anxiety in children has increased over time. In 1950, the average score on the Child Manifest Anxiety Scale was µ= 15.1. A sample of n = 16 was taken from children today, which produced a mean anxiety score of M= 23.3 with SS= 240. Based on the sample, has there been a significant change in the average level of childhood anxiety since 1950? (Use a 2-tailed test with α= .05) Write a sentence describing the outcome of the hypothesis test as it would appear in a research report.
- Zanele has just begun her new job as on the sales force of a very competitive company. In a sample of 16 sales calls it was found that she closed the contract for an average value of R108 with a standard deviation of R12. Test at 5% significance that the population mean is at least R100 and against the alternative that it is less than R100. Company policy requires that new members of the sales force must exceed an average of R100 per contract during the trial employment period. Can we conclude that Zanele has met this requirement at the significance level of 95%?You are conducting a study to see if the accuracy rate for fingerprint identification is significantly less than 0.24. Thus you are performing a left-tailed test. Your sample data produce the test statistic z=−2.287z=-2.287. Find the p-value accurate to 4 decimal places.p-value =You are conducting a study to see if the accuracy rate for fingerprint identification is significantly less than 0.22. Thus you are performing a left-tailed test. Your sample data produce the test statistic z=−2.653z=-2.653. Find the p-value accurate to 4 decimal places.
- The recommended daily dietary allowance for zinc among males older than age 50 years is 15 mg/day. An article reports the following summary data on intake for a sample of males age 65−74 years: n = 116, x = 12.5, and s = 6.35. Does this data indicate that average daily zinc intake in the population of all males age 65−74 falls below the recommended allowance? (Use ? = 0.05.)State the appropriate null and alternative hypotheses. H0: ? = 15Ha: ? ≠ 15H0: ? = 15Ha: ? > 15 H0: ? = 15Ha: ? ≤ 15H0: ? = 15Ha: ? < 15 Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) z = P-value = State the conclusion in the problem context. Do not reject the null hypothesis. There is not sufficient evidence that average daily zinc intake falls below 15 mg/day.Reject the null hypothesis. There is not sufficient evidence that average daily zinc intake falls below 15 mg/day. Do not reject…You are conducting a study to see if the proportion of women over 40 who regularly have mammograms is significantly less than 0.66. Thus you are performing a left-tailed test. Your sample data produce the test statistic z=−1.812z=-1.812. Find the p-value accurate to 4 decimal places.The business school at Wassamatta U. receives a large number of applicants to its undergraduate honors program in economics. This photo shows the GPA's of a sample of 260 applicants that have applied to the program in the last several years. From the data the mean GPA is x = 3.13 with standard deviation s = 0.395 1) If a normal model N(3.13,0.395) is an appropriate model for the GPA's of all applicants to the undergraduate honors program in economics, what is the probability that an applicant's GPA is 3.25 or greater? Use three decimal places. 2) what is the actual proportion (a decimal number between 0 and 1) of GPA's in the data that are 3.25 or greater? GPA bins 3.24 2.375 3.63 2.5 3.35 2.625 2.93 2.75 3.26 2.875 3.02 3 3.75 3.125 3.48 3.25 2.77 3.375 2.78 3.5 3.18 3.625 3.58 3.75 2.96 3.875 2.76 4 3.32 3.03 3.18 3.07 3.10 2.88 2.40 3.19 3.16 3.01 2.99…
- Einar Óli has measured the area of scallops on two places in Breiðafjörður and used a t-test to investigate whether there is a difference in the area of scallops in those two places. A type-ll error occurred when Einar Óli conducted his hypothesis test. What happened? 1. There is no difference in the average area of scallops at those two places but Einar Óli rejected the alternative hypothesis and concluded that there difference. 2. There is no difference in the average area of scallops at those two places but Einar Óli concluded that there is a difference. 3. There is no difference in the average area of scallops at those two places but Einar Óli made no claims. 4. There is a difference in the average area of scallops at those two places but Einar Óli made no claims. 5. OR-command:The recommended daily dietary allowance for zinc among males older than age 50 years is 15 mg/day. An article reports the following summary data on intake for a sample of males age 65−74 years: n = 111, x = 12.4, and s = 6.69. Does this data indicate that average daily zinc intake in the population of all males age 65−74 falls below the recommended allowance? (Use ? = 0.05.)State the appropriate null and alternative hypotheses. H0: ? = 15Ha: ? > 15H0: ? = 15Ha: ? < 15 H0: ? = 15Ha: ? ≤ 15H0: ? = 15Ha: ? ≠ 15 Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) z = P-value = State the conclusion in the problem context. Do not reject the null hypothesis. There is sufficient evidence that average daily zinc intake falls below 15 mg/day.Reject the null hypothesis. There is sufficient evidence that average daily zinc intake falls below 15 mg/day. Do not reject the null…The research question is whether attractiveness affects the behavior of infants lookingat photographs of women’s faces. The researcher is expecting the infants to prefer themore attractive face. Therefore, the researcher predicts that the infants will spendmore than half of the 20-second period looking at the attractive face. Specifically, the researcher tested a sample of n = 9 infants and obtained a mean of M = 13 seconds looking at the attractive face with SS = 72 Calculate the t statistic and show your work.