STOR 155Review questions for Statistical inference for sample meanQuestion 1• Determine whether each of the following statements is true or false. • A) The margin of error for a 95% confidence interval for the mean μ increases as the sample size increases. • B) The margin of error for a confidence interval for the mean μ, based on a specified sample size n, increases as the confidence level decreases. • C)The margin of error for a 95% confidence interval for the mean μ decreases as the population standard deviation decreases. • D)The sample size required to obtain a confidence interval of specified margin of error m increases as the confidence level increases.• Answer:• A) False, B) False, C) True, D) TrueQuestion 2• A) 90%• B) 95%• C) 99%• D) 99.9%• Answer: CQuestion 3Chocolate bars produced by a certain machine are labeled 8.0 oz. The distribution of the actual weights of these chocolate bars is claimed to be Normal with a mean of 8.1 oz and a standard deviation of 0.1 oz. • A quality control manager initially plans to take a simple random sample of size n from the production line. If he were to double his sample size (to 2n), by what factor would the standard deviation of the sampling distribution of the sample mean change? • A) 1/2 B) • C) D) 2• Answer: BQuestion 4• If the quality control manager takes a simple random sample of ten chocolate bars from the production line, what is the probability that the sample mean weight of the ten sampled chocolate bars will be less than 8.0 oz?• A) 0• B) 0.0008• C) 0.0316• D) 0.1587Answer: BQuestion 5• The following histogram shows the distribution of 1000 sample observations from a population with mean μ = 4 and variance σ2= 8 • Suppose a simple random sample of 100 observations is to be selected from the population and the sample average, , calculated. Which of the following statements about the distribution of the sample mean is (are) FALSE?• A)The distribution of will have mean 4.• B)The distribution will be approximately Normal.• C)Because the distribution shown in the histogram above is clearly skewed to the right, the shape of the distribution of will also show skewness to the right.• D)Even though the distribution of the population variable appears to be skewed to the right the distribution of will be approximately symmetric around μ = 4.• E)The standard deviation of the distribution of will be 0.283.• Answer: CQuestion 6• In the construction industry, compressive strength of concrete is a crucial characteristic. Suppose for a particular residential construction job the concrete tested after 3 days should have a mean compression strength of μ = 3000 psi with a standard deviation of σ = 50 psi. It is known that compressive strength of concrete is Normally distributed. On a construction site a sample of n = 5 specimens is selected and tested after 3 days. If the concrete has the desired characteristics what is the probability that the sample mean will be larger than 3060 psi?• A) 0.996 B) 0.004 C) 0.885 D) 0.115• E) Unable to determine because the sample size n = 5 is much too small to rely on the Normal distribution for calculation of the required probability.• Answer:BQuestion 7What is the standardized Z-Statistic?What is the P-Value?Question 8• The square footage of the several thousand apartments in a new development is advertised to be 1250 square feet, on average. A tenant group thinks that the apartments are smaller than advertised. They hire an engineer to measure a sample of apartments to test their suspicions. Let μ represent the true average area (in square feet) of these apartments. What are the appropriate null and alternative hypotheses? • A) H0: μ = 1250 vs. Ha: μ < 1250• B) H0: μ = 1250 vs. Ha: μ ≠ 1250• C) H0: μ = 1250 vs. Ha: μ > 1250• Answer: AQuestion 9Suppose we wish to test the hypotheses H0: μ = 10 versus Ha: μ < 10, where μ represents the mean age of non-high school aged children who are members of a large gymnastics club in a metropolitan area. Assume age follows a Normal distribution with σ = 2. A random sample of 16 ages is drawn from the population, and we find the sample mean of these observations to be = 8.76. • What is the value of the test statistic?• A) z = –0.62• B) z = –1.24• C) z = –2.48• D) z = –9.92• Answer: CQuestion 10• What is the value of the P-value?• A) 0• B) 0.0066 • C) 0.1075• D) 0.2676• Answer: BQuestion 11What are the Null and Alternative hypothesisThe data result in an average of 22 parts per million. What is the standardized Z-statistic ?What is the P-value?Question 12Question 13What is a 95% confidence interval ?If not 400 but 100 sophomores were measured how would this affect the confidence interval ?Suppose you wanted to estimate the population mean within a margin of error of .001 with a 95% confidence interval. What sample size would you take?Question 14Ten medium oranges will be randomly selected from a package. What is the sampling distribution of the sample mean weight of a random sample of ten medium oranges?Ten medium oranges will be randomly selected from a package. What is the sampling distribution of the number of oranges in the sample that weigh more than 14 oz?THE WEIGHTS OF MEDIUM ORANGES PACKAGED BY AN ORCHARD ARE NORMALLY DISTRIBUTED WITH A MEAN OF 14 OZ AND A STANDARD DEVIATION OF 2
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