Exam 8: Drawing Inferences From Large Samples

A parameter is a numerical feature of a probability distribution.

The baggage manager of an airport wants to improve the time that passengers wait in the baggage claim area. She has a sample of 129 domestic flights. The mean waiting time is $\bar{x}$ = 12 minutes and s = 3.6 minutes. Is the claim that μ>13.5 minutes substantiated by these data? Test with α = 0.01.

Out of a sample of 500 students, 401 owned a smart phone that was less than 3 years old. Obtain the estimated standard error. Round your answer to three decimal places.

The research department of a biochemical industry took a sample of 60 bacteria cultures of the same kind and observed that the mean weight was 25.267 grams with standard deviation of 8.816 grams. Obtain a 99% confidence interval for the mean weight of the bacteria cultures.

The following summary of a data set refers to the girth of grizzly bears in centimenters. Find the 94% error margin. Round your answer to two decimal places.

A survey is conducted of n = 957 adults (65 years or older) and x = 258 reported high blood pressure problems. A) Provide a point estimate of p. Round your answer to three decimal places. B) Determine the 96% error margin. Round your answer to four decimal places.

An inspection of eight wind turbines revealed that 13 operate too loudly according to new sound restrictions. The summary statistics are n = 80 x = 13 Let p = population proportion that are too loud. (a) Give a point estimate of p and its estimated standard error (b) Obtain a 95 % confidence interval for the population mean p. (c) Does your interval cover p? Explain.

Assuming the population is normal and $\mu$ is known, a 98% confidence interval for $\mu$ is given by

The number of times an undergraduate binge watched a TV se- ries in the past month was recorded for a sample of size 49. The summary statistics are n = 49 $\bar{x}$ = 2.1 s = 1.61 Let µ =population mean number of times. (a) Conduct a test of hypotheses with the intent of showing that µ > 1.5. Take α = .05. (b) Calculate the P-value. Does this strengthen your conclusion to the test of hypotheses? Explain. (c) Based on the conclusion to your test in Part a, what error could you have made.

When estimating the mean of a population, how large a sample is required in order that 96% error margin be $\frac{1}{20}$ of the population standard deviation?

When using $\bar{x}$ to estimate μ , find the standard error for n = 160, σ =51 . Round your answer to three decimal places.

When estimating the mean of a population, how large a sample is required in order that the 94% error margin be 14% of the population standard deviation?

When using $\bar{x}$ to estimate μ find the 100 (1-α)% error margin for n = 146 σ =63 98% error margin. Round your answer to three decimal places.

Given the standard deviation σ, the statement of your claim about μ , the sample size, and the desired level of significance α. Formulate: a) the hypotheses, b) the test statistic Z, c) the rejection region.

An industrial researcher wants to perform a test with the intent of establishing that this company's compact fluorescent lamp has a mean life greater than 7100 hours. The sample size is 128 and he knows that $\sigma$ =79 hours. Find the numerical value of c so that the test has a 5% level of significance.

The number of times an undergraduate binge watched a TV se- ries in the past month was recorded for a sample of size 49. The summary statistics are n = 49 $\bar{x}$ = 2.1 s = 1.61 Let µ =population mean number of times. (a) Give a point estimate of µ and its estimated standard error. (b) Obtain a 95 % confidence interval for the population mean µ. (c) Does your interval cover µ? Explain

Given the standard deviation σ, the statement of your claim about μ, the sample size, and the desired level of significance α. Formulate: a) the hypotheses, b) the test statistic Z, c) the rejection region.

Assume n = 38, $\bar{x}$ = 23.367, and s = 11.056. Obtain a 98% confidence interval for μ, the population mean.

Suppose $\bar{x}$ = 4.55 and s = 5.17 for N = 40. We claim that H₀ = 2.3 and H₁ ≠ 2.3 . Find the P- value. Round your answer to four decimal places.

A random sample of 781 applicants for drivers license was taken, 270 of the applicants failed the driving test. Find a 90% confidence interval for the corresponding population proportion.