# QUANTITATIVE METHODS IN ECONOMICS

Suppose that a florist wanted to compare the mean price per order of sales on February 13 and February 14. She selected random samples of 25 orders on February 13 and 20 orders on February 15. Assume equal standard deviations for the populations from where the samples were taken. How many degrees of freedom will the resulting t statistic have?

Question 1 options:

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Suppose the researcher had wished to test the hypotheses that whether hotel room daily rates in Manitoba are higher than Alberta

H0: u1 = u2, Hau1 > u2.

Suppose further that in a similar set of sample data, the P value for the two-sample test statistic is 0.002 and α is chosen to be 0.01. The researcher should conclude that:

Question 2 options:

 there is statistically significant evidence that average daily hotel room rates in Manitoba are higher than in Alberta. there is no statistically significant evidence that there is a difference in average daily hotel room rates in Manitoba and Alberta. there is statistically significant evidence that average daily hotel room rates in Manitoba are lower than in Alberta. there is statistically significant evidence that there is no difference in average daily hotel room rates in Manitoba and Alberta.

The z statistic has a value between ±1.96. This implies that the two-sided p-value is greater than 0.05.

Question 3 options:

 True False

In a statistical test of hypotheses, we say the data are statistically significant at level α (alpha) if:

Question 4 options:

 α is small the P value is larger than α the P value is less than α α = .05

When performing a t-test for means, the Power of the test will increase when:

Question 5 options:

 the sample size(s) decrease(s) the level of significance increases the sample size(s) increase(s)

α is the probability of committing a Type I error.

Question 6 options:

 True False

The one-side p-value cannot be greater than 0.5

Question 7 options:

 True False

If the z statistic has a value between ±1.96 this implies that the two-sided p-value is greater than 0.05.

Question 8 options:

 True False

A higher significance level indicates greater risk of making a Type I error.

Question 9 options:

 True False

As the sample size increases its widen the confidence interval.

Question 10 options:

 True False

When planning a study from which you will calculate a confidence interval, your goal should be to have a confidence interval that has:

Question 11 options:

 a high confidence level and a low margin of error. a high confidence level and a high margin of error. a low confidence level and a high margin of error. a low confidence level and a low margin of error.

Jack, measure the weights of a random sample of 400 male students and construct a 95% confidence interval. The sample mean is 176.2 lbs. Suppose that the weights of male students follow a normal distribution with known standard deviation σ = 11.1 lbs. Suppose Smith compute a 95% confidence interval for the mean from a random sample based on 100 rather than 400 students. Which of the following statements is true?

Question 12 options:

 The margin of error would be larger for Smith’s measure than Jack’s. Sigma (σ) would decrease. The margin of error would be the same because the level of confidence has not changed. The margin of error would be smaller for Smith’s measure than Jack’s.

The one-sample t statistic from a sample of n = 19 observations for the two-sided test of

H0: μ = 6, Ha: μ ≠ 6

has a p-value of 0.026. Based on this information, which of the following is true?

Question 13 options:

 We would reject the null hypothesis at α = 0.01. We would not reject the null hypothesis at α = 0.05. We would reject the null hypothesis at α = 0.05. Not enough information to tell.

The one-sample t statistic from a sample of n = 19 observations for the two-sided test of

H0: μ = 6, Ha: μ ≠ 6

has a value t = −1.75 Based on this information, which of the following is true?

Question 14 options:

 We would reject the null hypothesis at α = 0.05. We failed to reject the null hypothesis at either significance levels as above. Not enough information to tell. We would reject the null hypothesis at α = 0.01.

Smart shopping carts are shopping carts equipped with scanners that track the total cost of the items in the cart. While both consumers and retailers have expressed interest in the use of this technology, actual implementation has been slow. It was calculated a 95% confidence interval for the mean difference in spending when shopping with and without real-time feedback. The 95% margin of error was roughly \$6.70. Suppose that a new study being planned and the desired margin of error is \$4.5 and the sample standard deviations are both \$17. (1) How many shoppers per group we need (round up)? (2) If we reduce the desired margin of error is \$3.1 instead of \$4.5 then what would be the new sample size (round up)?

Question 15 options:

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Population mean is an essential piece of information for choosing t-test over z-test.

Question 16 options:

 True False

When formulating the null and alternative hypothesis for a test of significance, you should:

Question 17 options:

 always look at the sample data to determine whether a one sided or a two sided test should be used. use a two sided test if you do not have a specific direction firmly in mind in advance. avoid using one sided tests. always use a two sided test.

A hypothesis test is conducted and the null hypothesis is rejected at the 5% significance level. If the significance level is decreased to 1%:

Question 18 options:

 the P value will get smaller. the null hypothesis would still be rejected. the null hypothesis would now not be rejected. the null hypothesis might be rejected or it might not be rejected.

An SRS of 100 items taken from a particular population having σ = 30 is used to test the hypotheses H0: µ = 500, Haµ ≠ 500.

If the sample average is 495.5, which of the following drawings of the sampling distribution of X correctly depicts the P value for the test (4 decimal point)? Based on the p-value, take decision and then make a conclusion for the policy makers.

Question 19 options:

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The standard error of the sample mean is defined

Question 20 options:

 σ sn σn√

Recent reports indicate that the average household in the United States has 2.5 television sets. Suppose that in a sample of 25 households, the average number of television sets is 2.9 with a standard deviation of 0.85. 1) The standard error of the sample mean is: (two decimal); 2) what would be the effect (increase, decreases, no change) on standard error if sample size increases? 3) what would be the effect (increase, decreases, no change) on standard error if average television set increases 2.5 to 3.0 per households?

Question 21 options:

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Which of the following statements is true if the 99% confidence interval is used to test H0: µ = 4 cm, Haµ ≠ 4 cm?

Question 22 options:

 The P value of the test is larger than 0.01. The P value of the test is smaller than 0.01. The probability that the mean diameter is not 4 cm is 0.99. There is not significant evidence that the mean diameter is not 4 cm.

Suppose the researcher had wished to test the hypotheses (m1=uber fare; m2=texi fare)

H0: m1 = m2, Ham1 > m2.

Suppose further that in a similar set of sample data, the P value for the two sample test statistic is 0.002 and α is chosen to be 0.01. The researcher should conclude that:

Question 23 options:

These days, the battery life of a smartphone is more important than ever: demanding apps, bigger screens, and an increased reliance on smartphones have all contributed to the need to change a phone at least once daily. The web-surfing test reports calculated the average battery life of your smartphone with 95% confidence interval.The margin of error based on an SRS of n=25 days was 36 minutes. Suppose that a new study is being planned and the goal is to have a margin of error 20 minutes. How many days do you need (round up)? The sample standard deviation was 45 minutes and population standard deviation was 35 minutes.

Question 24 options:

The question of interest is whether to invest on 10 years bond (bond10) or 7 years bond (bond7). We want to compare the return from bond10 and bond7 using test3 data. It is assumed that bond10 will have higher return compared to bond7, does this true with α

1) formulate hypothesis

2) Decision

3) Conclusion

Question 25 options:

 Blank # 1 Blank # 2 Blank # 3

The question of interest is whether to invest on 10 years bond (bond10) or 7 years bond (bond7). We want to compare the return from bond10 and bond7 using test3 data. It is assumed that bond10 will have higher return compared to bond7, does this true with α{“version”:”1.1″,”math”:”<math xmlns=”http://www.w3.org/1998/Math/MathML”><mi>α</mi>[/itex]”}=0.05?

1) formulate hypothesis

2) Decision

3) Conclusion

Question 25 options:

 Blank # 1 Blank # 2 Blank # 3

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