# A state school administrator claims that the standard deviation of test scores for 8th grade students who took a life-science assessment test is at most 35.

For 20 points

1. A state school administrator claims that the standard deviation of test scores for 8th grade students who took a life-science assessment test is at most 35. You work for the administrator and you are asked to test this claim. You find that a random sample of size 36 tests that you collected has a standard deviation of 37.6. At α = 0.1, do you have enough evidence to support the administrator’s claim? Assume test scores are normally distributed. Please show all 5 steps involved

For 15 points

1. In a simple random sample of 30 luxury cars, the sample average annual fuel cost was \$5425 and a sample standard deviation of \$807.55. Construct the 90% confidence interval for the population mean. Assume that the annual fuel cost is normally distributed. Please interpret your result. Please show all work
2. 15 points)

The reading speed of sixth-grade students is approximately normal, with a mean of 138 words per minute and a standard deviation of 27 words per minutes.

1. What is the probability that a randomly selected sixth-grade student reads more than 118 word per minute?

1. What is the probability that a randomly selected sixth-grade student reads less than 140 words per minute?

1. What is the probability that a randomly selected sixth-grade student will read between 118 words and 168 words per minute?

1. What is the reading speed of a sixth-grade student that separate the lower 80% to the rest of sixth grade students?

1. What reading speeds separate the middle 74% of reading speed of sixth-grade students to the rest?

For 20 points

For 20 points

1. According to a survey conducted by the vegetarian Digest, it has been claimed that less than 78% of American adults eat salad once or more times per week. Christian Frederic, a reputable trainer and nutritionist, is disputing the claim by the vegetarian Digest. He conducted a survey of 275 adults in America and finds that 205 of them eat salad once or more times per week. Conduct the appropriate test addressing the nutritionist’s suspicions. Use a 0.01 level of significance. Please show all 5 steps involved

For 15 points

1. You wish to estimate, with a 74% confidence, the population proportion of Metaluna Adults who think they have a comfortable saving account. Your estimate must be accurate within 4.6% of the population proportion.
1. No preliminary estimate is available. Find the minimum sample size needed.
2. Find the minimum sample size needed, using a prior estimate that found that 33.33% of U.S adults think that they have a comfortable saving account.

For 15 points

1. You randomly select and weigh 23 samples of an allergy medication. The sample standard deviation is 1.23 milligrams.  Assuming the weights are normally distributed, construct 80% confidence intervals for the population variance and standard deviation. Please interpret your result. Please show all work

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