Chapter 9 SG
In performing a hypothesis test where the null hypothesis is that the population mean is 4.8 against the alternative hypothesis that the population mean is not equal to 4.8, a random sample of 25 items is selected. The sample mean is 4.1 and the sample standard deviation is 1.4. It can be assumed that the population is normally distributed. The observed "t" value for this problem is _______.
-2.5
A political scientist wants to prove that a candidate is currently carrying more than 60% of the vote in the state. She has her assistants randomly sample 200 eligible voters in the state by telephone and only 90 declare that they support her candidate. The observed z value for this problem is _______.
-4.33
A company believes that it controls more than 30% of the total market share for one of its products. To prove this belief, a random sample of 144 purchases of this product is contacted. It is found that 50 of the 144 purchased this company's brand of the product. If a researcher wants to conduct a statistical test for this problem, the observed z value would be _______.
1.24
Suppose a researcher is testing a null hypothesis that μ = 61. A random sample of n = 36 is taken resulting in a sample mean of 63 and s = 9. The observed t value is _______.
1.33
In performing a hypothesis test where the null hypothesis is that the population mean is 23 against the alternative hypothesis that the population mean is not equal to 23, a random sample of 17 items is selected. The sample mean is 24.6 and the sample standard deviation is 3.3. It can be assumed that the population is normally distributed. The degrees of freedom associated with this are _______.
16
In performing a hypothesis test where the null hypothesis is that the population mean is 4.8 against the alternative hypothesis that the population mean is not equal to 4.8, a random sample of 25 items is selected. The sample mean is 4.1 and the sample standard deviation is 1.4. It can be assumed that the population is normally distributed. The degrees of freedom associated with this are _______.
24
If a company wants to prove that the proportion (p) of its revenues from overseas operations is more than 18%, the null and alternate hypotheses are __________.
H0: p = 0.18 and H1: p > 0.18
A study reported by Roper Starch Worldwide states that, on average, an influential person makes 5.8 recommendations about office equipment per year. You believe that this figure is too high and you want to test your belief.
One-Tailed
The results of a survey conducted by Purchasing revealed that the mean age of a purchasing manager is 46.2. This seems too young to you and you want to conduct a test to determine if the average age of a purchasing manager is older than 46.2.
One-Tailed
Maritz Marketing Research reports that 42% of all adults seek advice from others in selecting a lawyer. A business researcher wants to test this claim.
Two tailed
According to the U.S. Department of Labor Statistics Consumer Expenditure Survey, the average family spends $3,465 annually on meals at home. A business researcher would like to conduct a survey of families in her state to determine if this figure is true for her state, but she does not really have any idea whether or not the average might be higher or lower in her state.
Two-Tailed
In a hypothesis test, the test statistic computed from the sample data is considered extreme or significant if it is __________.
highly unlikely to occur due to chance
Consider the following null and alternative hypotheses. Ho: μ ≥ 67 Ha: μ < 67 These hypotheses _______________.
indicate a one-tailed test with a rejection area in the left tail
A small restaurant owner believes no more than 36 % of his customers travel over 10 miles to his business. He is interested in expanding his customer base through marketing. However, he would like to test his hypothesis prior to investing money in a marketing initiative. He intends to use the following null and alternative hypotheses. Ho: p ≤ 0.36 Ha: p > 0.36 These hypotheses _______________.
indicate a one-tailed test with a rejection area in the right tail
A small restaurant owner believes that more than 36 % of his customers would be willing to order take out service if it were available. He is interested in surveying his customer base to test this notion. He intends to use the following null and alternative hypotheses. Ho: p = 0.36 Ha: p > 0.36 These hypotheses _______________.
indicate a one-tailed test with a rejection area in the right tail
Consider the following null and alternative hypotheses. Ho: μ ≤67 Ha: μ > 67 These hypotheses _______________.
indicate a one-tailed test with a rejection area in the right tail
A small restaurant owner believes exactly 36 % of his customers come to the restaurant because of his daily half-price specials. He is interested in expanding his daily specials and increasing the price. However, he would like to test his hypothesis prior to expanding the daily special offerings. He intends to use the following null and alternative hypotheses. Ho: p = 0.36 Ha: p ≠ 0.36 These hypotheses _______________.
indicate a two-tailed test
Consider the following null and alternative hypotheses. Ho: μ = 67 Ha: μ ≠ 67 These hypotheses ______________.
indicate a two-tailed test
A statistically significant result __________.
may or may not be substantive
All statistical hypotheses consist of two parts, a null hypothesis and an alternate hypothesis. These two parts must be __________.
mutually exclusive and collectively exhaustive
Ophelia O'Brien, VP of Consumer Credit of American First Banks (AFB), monitors the default rate on personal loans at the AFB member banks. One of her standards is "no more than 5% of personal loans should be in default." On each Friday, the default rate is calculated for a sample of 500 personal loans. Last Friday's sample contained 30 defaulted loans. Ophelia's null hypothesis is _______.
p = 0.05
The executives of CareFree Insurance, Inc. feel that "a majority of our employees perceive a participatory management style at CareFree." A random sample of 200 CareFree employees is selected to test this hypothesis at the 0.05 level of significance. Eighty employees rate the management as participatory. The null hypothesis is __________.
p = 0.50
The null hypothesis in a hypothesis test contains a statement about the population parameter such as the population mean or population proportion. The decision to reject the null hypothesis will be made if the outcome of the study or the sample statistic such as sample mean or sample proportion is __________.
significantly different from the hypothesized value of the population parameter
A Type II error is committed when __________.
the null hypothesis is false and it is not rejected
A Type I error is committed when __________.
the null hypothesis is true and it is rejected
A company believes that it controls more than 30% of the total market share for one of its products. To prove this belief, a random sample of 144 purchases of this product is contacted. It is found that 50 of the 144 purchased this company's brand of the product. If a researcher wants to conduct a statistical test for this problem, the alternative hypothesis would be _______.
the population proportion is greater than 0.30
In the testing of hypotheses about the population proportion when the sample size is large enough to satisfy the central limit theorem the critical values are determined using the __________.
z-distribution
The weight of a USB flash drive is 30 grams and is normally distributed. Periodically, quality control inspectors at Dallas Flash Drives randomly select a sample of 17 USB flash drives. If the mean weight of the USB flash drives is too heavy or too light the machinery is shut down for adjustment; otherwise, the production process continues. The last sample showed a mean and standard deviation of 31.9 and 1.8 grams, respectively. . The null hypothesis is ______.
μ = 30
All statistical hypotheses consist of two parts, __________ and __________.
a null hypothesis; an alternate hypothesis
Generally speaking, new hypotheses that the business researchers want to "prove" are stated in the __________.
alternate hypothesis
In a one-sided test of the hypotheses about a population proportion, the p-value was found to be 0.045. The null hypothesis in this test would __________.
be rejected if the significance level is = 0.05