- A machine is designed to fill toothpaste tubes, on an average, with 5.8 ounces of toothpaste. The manufacturer does not want any underfilling or overfilling. The correct hypotheses to be tested are H0: μ = 5.8 Ha: μ ≠ 5.8.
- A sample of 200 elements from a population with a known standard deviation is selected. For an interval estimation of μ, the proper distribution to use is the normal distribution.
- A Type I error is committed when a true null hypothesis is rejected.
- An estimate of a population parameter that provides an interval of values believed to contain the value of the parameter is known as the interval estimate.
- An insurance company selected samples of clients under 18 years of age and over 18 and recorded the number of
accidents they had in the previous year. The results are shown below.
Under Age of 18 Over Age of 18
n1 = 500 n2 = 600
Number of accidents = 180 Number of accidents = 150
We are interested in determining if the accident proportions differ between the two age groups. Let pu represent the
proportion under and po the proportion over the age of 18. The null hypothesis is pu – po = 0. - As the number of degrees of freedom for a t distribution increases, the difference between the t distribution and the standard normal distribution becomes smaller.
- As the test statistic becomes larger, the p-value gets smaller
- For a lower tail test, the p-value is the probability of obtaining a value for the test statistic at least as small as that provided by the sample.
- For a two-tailed test, the p-value is the probability of obtaining a value for the test statistic as unlikely as that provided by the sample.
- For the following hypothesis test,
H0: μ ≥ 150
Ha: μ < 150
the test statistic can be either negative or positive. - From a population that is normally distributed, a sample of 25 elements is selected and the standard deviation of the sample is computed. For the interval estimation of μ, the proper distribution to use is the t distribution with 24 degrees of freedom
- From a population that is not normally distributed and whose standard deviation is not known, a sample of 6 items is selected to develop an interval estimate for the mean of the population (μ). The sample size must be increased.
- Generally, the ________ sample procedure for inferences about two population means provides better precision than the _______ sample approach. matched, independent
- If a hypothesis is rejected at 95% confidence, it will also be rejected at 90% confidence
- If the cost of making a Type I error is high, a smaller value should be chosen for the level of significance.
- If the null hypothesis is not rejected at the 5% level of significance, it will also not be rejected at the 1% level.
- If the null hypothesis is rejected at the .05 level of significance, it will always be rejected at the .10 level of significance.
- If the null hypothesis is rejected at the 5% level of significance, it may be rejected or not rejected at the 1% level.
- If the null hypothesis is rejected in hypothesis testing, the alternative hypothesis is true.
- If two independent large samples are taken from two populations, the sampling distribution of the difference between the two sample means can be approximated by a normal distribution.
- If we are interested in testing whether the mean of items in population 1 is larger than the mean of items in population 2, the alternative hypothesis should state μ1 – μ2 > 0
- If we are interested in testing whether the proportion of items in population 1 is larger than the proportion of items in alternative hypothesis should state p1 – p2 > 0.
- If we change a 95% confidence interval estimate to a 99% confidence interval estimate, we can expect the width of the confidence interval to increase.
- In a two-tailed hypothesis test, the area in each tail corresponding to the critical values is equal to α/2.
- In developing an interval estimate, if the population standard deviation is unknown the sample standard deviation must be used.
- In general, higher confidence levels provide wider confidence intervals.
- In hypothesis testing if the null hypothesis is rejected, the alternative hypothesis is true
- In hypothesis testing, if the null hypothesis has been rejected when the alternative hypothesis has been true, the correct decision has been made
- In hypothesis testing, the tentative assumption about the population parameter is the null hypothesis.
- In hypothesis tests about a population proportion, p0 represents the hypothesized population proportion.
- In hypothesis tests about p1 – p2, the pooled estimator of p is a(n) weighted average of pvar1 and pvar2
- Of the two production methods, a company wants to identify the method with the smaller population mean completion
time. One sample of workers is selected and each worker first uses one method and then uses the other method. The
sampling procedure being used to collect completion time data is based on matched samples - Regarding inferences about the difference between two population means, the sampling design that uses a pooled sample variance in cases of equal population standard deviations is based on independent samples.
- The ability of an interval estimate to contain the value of the population parameter is described by the confidence level.
- The academic planner of a university thinks that at least 35% of the entire student body attends summer school. The correct set of hypotheses to test his belief is H0: p .35 Ha: p < .35.
- the level of significance is the maximum allowable probability of Type I error.
- The mean of the t distribution is 0
- The probability that the interval estimation procedure will generate an interval that does not contain the actual value of the population parameter being estimated is the same as α
- The p-value is a probability
- The sampling distribution of pvar1-pvar2 is approximated by a normal distribution.
- The standard error of xvar1-xvar2 is the standard deviation of the sampling distribution of
- The sum of the values of α and β is not needed in hypothesis testing.
- The t distribution should be used whenever the sample standard deviation is used to estimate the population standard deviation.
- To compute the minimum sample size for an interval estimate of l , we must first determine all of the following except degrees of freedom.
- To compute the necessary sample size for an interval estimate of a population mean, all of the following procedures are recommended when σ is unknown except use .5 as an estimate
- Two approaches to drawing a conclusion in a hypothesis test are p-value and critical value.
- Using an α = .04, a confidence interval for a population proportion is determined to be .65 to .75. For the same data, if α is decreased, the confidence interval for the population proportion becomes wider.
- We can reduce the margin of error in an interval estimate of p by doing any of the following except increasing the planning value p* to .5.
- When developing an interval estimate for the difference between two population means with sample sizes of n1 and n2, n1 and n2 can be of different sizes.
- When each data value in one sample is matched with a corresponding data value in another sample, the samples are known as matched samples.
- When the area corresponding to the critical value is in the lower tail of the sampling distribution, the p-value is the area under the curve less than or equal to the test statistic.
- When the following hypotheses are being tested at a level of significance of α
H0: μ 500
Ha: μ < 500
the null hypothesis will be rejected, if the p-value is α. - When the level of confidence decreases, the margin of error becomes smaller
- When the null hypothesis is rejected, it is possible a Type I error has occurred.
- Which of the following does not need to be known in order to compute the
p-value? the level of significance
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