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Test of Significance ReviewName:Date:For each question, identify if it is (a) t-test, or (b) proportion z-test. Identify Ho and Ha. Find your p-value and write your conclusion. Hint: There are 4 t-tests and 6 proportions. There are 5 α>p and 5 p>αPossible p-values:.1188.55151.0125.0045.0746.0336.0385.009.0043LeJon Brames, a starting player on a local basketball team, made only 40% of his free throws last season. Hoping to improve his chances at landing a college scholarship, he worked on developing a softer shot to improve his free throw accuracy. In the first 15 games, LeJon made 51 free throws in 80 attempts. Has LeJon improved? Use ? = .01A Telktronics dental X-ray machine bears a label stating that the machine gives radiation dosages with a mean of less than 5.00 milliroentgens. Sample data consist of 46 randomly selected observations with a mean of 4.23 milliroentgens and a standard deviation of 1.91 milliroentgens. Using a 0.01 level of significance, test the claim stated on the label.An Internet server claimed that its users averaged 13 hours per week. To determine whether this was an overstatement, a competitor conducted a survey of 55 customers and found that the average time spent online was 11.3 hours per week with a standard deviation of 5.2 hours. If Ha: ? < 13, show the calculations for the t-score and state the corresponding p-value. Write the conclusion based on part (a) using a 1% significance level.We often judge other people by their faces. It appears that some people judge candidates for elected office by their faces. Psychologists showed head-and-shoulders photos of the two main candidates in 32 races for the U.S. Senate to many subjects (dropping subjects who recognized one or both of the candidates) to see which candidate was rated “more competent” based on nothing but the photos (order of photos was random). On election day, the candidate whose face looked more competent won 21 of the 32 contests. If faces don’t influence voting, half of all races in the long run should be won by the candidate with the better face. Is there evidence that the candidate with the “more competent” face wins half the time? ? = .05A new formula for the propellant of missiles is being tested to determine if it is superior to the current formula. From past experience, the mean distance traveled has been 340 miles and was normally distributed. Ten randomly selected missiles with the new propellant are fired into the Pacific Ocean and produce an average distance of 348 miles with a standard deviation of 20. Does this prove that the distance has increased? Let ??= .05.When home runs abound in baseball, there are often charges that the new baseballs are “juiced” to travel further. Tests of the old balls showed that when dropped 24 ft onto a concrete surface, they bounced an average of 92.84 in. A test of a random sample of 40 new balls, the bounce heights had a mean of 92.67 in. with a standard deviation of 1.79 in. Let ? = .05. Test the claim that the new balls have bounce heights different from 92.84 inA new radar device is being considered for a certain defense missile system. The system is checked by experimenting with actual aircraft in which a kill or a no kill is randomly simulated. The claim of the current company states that the probability of a kill with the new system does not exceed the 0.8 probability of the existing device. If in 300 trials with the new radar device there were 250 kills, does the current company’s claim have merit? Use ? = .01.Is Elvis alive? USA Today ran a report about a University of North Carolina poll of a random sample of 1248 adults from the southern United States. It was reported that 8% of those surveyed believe that Elvis Presley still lives. The article began with the claim that “almost 1 out of 10” Southerners still thinks Elvis is alive. At the 0.01 significance level, test the claim that the true percentage is less than 10%. Ten engineering schools in the U.S. were surveyed. The random sample contained 175 chemical engineers. Of these students, 40 were female. Compute a 90% confidence interval for the true proportion of chemical engineering student who were female.A study was done to determine if 12-15 year old girls who want to be engineers differ in IQ from the average of all girls. The mean IQ of all girls in this age range is known to be about 100. A random sample of 49 girls is selected, who state that they want to be engineers and their IQ is measures. The mean IQ of the girls in the sample is 104.5 with a standard deviation of 14.4. Does this finding provide evidence, at the 0.05 level of significance, that the mean IQ of 12 – 15 year old girls who want to be engineers differs from the average? ................
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