Show that the significant value of t at level of significance ߙ for one-tailed test is equal to that of t at 2ߙ significance level for two-tailed test.
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(a) Show that the significant value of t at level of significance ߙ for one-tailed test is equal to that
of t at 2ߙ significance level for two-tailed test.
Consider the critical value at the level of significance α = 0.05 for a one tailed test.
Consider the critical value at the level of significance 2α = 0.1 for a two tailed test.
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- The mean number of English courses taken in a two-year time period by male and female college students is believed to be about the same. An experiment is conducted and data are collected from 24 males and 26 females. The males took an average of 4.2 English courses with a standard deviation of 1.1. The females took an average of 3.9 English courses with a standard deviation of 0.7. Conduct a hypothesis test at the 4% level of significance to determine whether the means are statistically the same. Step 1: State the null and alternative hypotheses. Ho: H1 = V H.: H1 – µ2 # v test.) (So we will be performing a two-taileda consumer advocay group tests the mean vitamin c content of 50 different brands of bottled juices using, in each case, a t-test of significance in which the null hypothesis is the mean amount of vitamin c that is on the nutrition facts label for that brand of juice. they find that two of the juice brands have statistically signifanctly lower vitamin c than claimed at the a 0.05 level. Is this an important discovery? Explain.From a research survey, it was found that a random sample of 22 high school graduates of an exclusive school has a mean NSAT score of 90 with a standard deviation of 16, while a random sample of 24 high school graduates of a public school showed a mean NSAT score of 85 with a standard deviation of 12. Is there a significant difference in the NSAT performance of these two groups of high school graduates? Use 5% level of significance. 1. What is the conclusion in problem
- A large software company gives job applicants a test of programming ability, and the mean score for the test has been 150 in the past. Twenty-five applicants are randomly selected from one large university and they produce a mean score of 155, with a standard deviation of 12. At a significance level of 0.025, does this indicate that the sample comes from a population with a mean score greater than 150 Interpret the random variable X using the context of the problem Interpret the random variable using the context of the problem Use proper notations to write the Null and Alternative Hypothesis What is the sample size? What is the population standard deviation? What is the sample standard deviation? Calculate the test statistic Find the p-value? Why did you make the decision in 10)?A study was designed to investigate the effects of two variables - (1) a studentʹs level of mathematical anxiety (2) teaching method - on a studentʹs achievement in a mathematics course. Students who had a low level of mathematical anxiety were taught using the traditional expository method. These students obtained a mean score of 290 with a standard deviation of 50 on a standardized test. Assuming no information concerning the shape of the distribution is known, what percentage of the students scored between 190 and 390? Group of answer choices At least 68% At least 95% At least 75% At least 88.9%A leasing firm claims that the mean number of miles driven annually, u, in its leased cars is less than 13,100 miles. A random sample of 50 cars leased from this firm had a mean of 13,003 annual miles driven. It is known that the population standard deviation of the number of miles driven in cars from this firm is 1120 miles. Is there support for the firm's claim at the 0.05 level of significance? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places, and round your responses as specified below. (If necessary, consult a list of formulas.) (a) State the null hypothesis H, and the alternative hypothesis H,. Ho :0 S H : (b) Determine the type of test statistic to use. (Choose one) D=0 (c) Find the value of the test statistic. (Round to three or more decimal places.) O#0 OO (d) Find the p-value. (Round to three or more decimal places.) (e) Can we support the leasing firm's claim that the mean number of miles driven…
- "On the Standford-Binet test, the mean IQ is 100. A class of 7 kindergarten pupils were tested with a resulting mean of 103 and a standard deviation of 5.28. Does this group have a mean significantly different than the norm group? Use 0.1 as your level of significance." It is safe to assume that they are within the norm unless additional evidence say otherwise. B "Yes, however, the class is lower than the norm, on average" "Yes, in fact the class is above the norm, on average." D) "No, I am 100% sure that they are within the norm value."A random sample of 100 private companies locating in Ankara was asked to rate on a scale from 1 (not important) to 5 (extremely important) for having the practical knowledge of statistics as a good job candidate. The sample mean rating was 4.7. a)Test at the 5% significance level the null hypothesis that the population mean rating is less than or equal to 4.5 against the alternative that it is greater than 4.5. Population variance is known as 0.6. b)Compute p-value and explain what the calculated p-value means.In a psychological experiment, 36 people (subjects) are selected randomly. The variableof interest is their reaction time to a particular stimulus (in seconds). Historical datastates that the variance in reaction times is 4 sec2and that the distribution of reactiontimes is approximately normal. The average time for the randomly selected subjects is6.2 seconds. What is the point estimate of this study? Based on this information, construct a 99% confidence interval for themean reaction time. Interpret the confidence interval that you obtained in (b).
- The manufacturer of the X-15 steel-belted redial truck tire claims that the mean mileage the tire can be driven before the tread wears out is 60,000 miles. Crosset Truck Company bought a sample of 48 tires and found that the mean mileage for its trucks is 59,000 miles (i.e. less than the manufacturer’s claim) with a standard deviation of 5,000 miles. Test the manufacturer’s claim at a significance level (α) equals 5%. Would your answer in (1) change if significance level become 10%? Would your answer in (1) change if the probability of type I error equals zero? Justify your answer If the same sample results had been obtained from a random sample of 125 tires, could your decision about the manufacturer’s claim changed using α=0.01 and comment on the results. Based on the sample size in (4), construct a 95% confidence level for the mean of mileage and comment on the results.In a random sample of males, it was found that 21 write with their left hands and 210 do not. In a random sample of females, it was found that 56 write with their left hands and 440 do not. Use a 0.05 significance level to test the claim that the rate of left-handedness among males is less than that among females. Identify the test statistic. and p valueScores on a certain "IQ" test for 18-25 year olds are normally distributed. A researcher believes that the average IQ score for students at a certain NJ college is less than 110 points, and so wants to test this hypothesis. The researcher obtain a SRS of 45 student IQ scores from school records and found the mean of the 45 results was 108 with a sample standard deviation of 21. The level of significance (alpha) used for this problem is 0.05/ What is the appropriate test statistic (Student must complete by showing by formula using the ap- propriate values in that formula "showing work" and the final answer and appropriate label)? O T test score = (108-110)/(45/sqrt(21)) = -.2037 O I test score = (108-110)/(21/sqrt(45)) = -.639 T test score = (108-110)/(21/sqrt(45)) = .639 I test score = (110-108)/(21/sqrt(45)) = .639