STAB22H3 Chapter Notes - Chapter 18 - 20: Null Hypothesis, Alternative Hypothesis, Confidence Interval

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10 Dec 2016

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Null hypothesis (h0): is a value for a parameter. Alternative hypothesis (ha): what you"re trying to prove. One-sided test: key words are larger and smaller than. Two-sided test: key words are different from. If the p value is big, don"t reject the null (more than 0. 05) If it is small, reject the null (less than 0. 05) Chapter 19: tests and confidence intervals for the population mean. Hypothesis test for mean: determine the null hypothesis and the alternative hypothesis: = sample mean: calculate a test. 0 = population mean: determine the p-value. statistic: (null/alternative) Curve changes the larger the sample size. As the p-values get smaller, the t-values get bigger: make a conclusion based on the p-value and the context of the problem. Big p-value (greater than 0. 05) = fail to reject null. Small p-value (less than 0. 05) = reject the null. If it is 95%, each tail is 2. 5%, since overall there is 5% in the tails all together.

Related Questions

Choose the best answer.

Suppose you collect a sample that has a mean of 37 with a 99% confidence interval of [32,42], and you are interested in the hypothesis test below at the α=0.05 level.

H0: μ=43

Ha: μ≠43

a) You should ask for more information because the sample size and standard deviation are needed for a hypothesis test of this kind.

b) You should fail to reject the null hypothesis because the p-value is greater than 0.05.

c) You should ask for more information because the confidence interval does not match the αα level.

d) You should reject the null hypothesis because the p-value is less than 0.05.

coffeegoat329

Use the following scenario for questions 6 – 8. In 2016-17, the average SAT score of the UVA first year class was 1420 out of 1600. An advisor in the statistics department is interested in determining whether statistics majors from that class have higher SAT scores than the average. He tests H,:µ = 1420 against Hạ: µ > 1420, where u is the mean SAT score for statistics majors from the 2016-17 first year class. In a simple random sample of 30 statistics majors, he finds a sample mean SAT score of 1440 with sample standard deviation of 40.

6. What is the value of the test statistic for this significance test?

a. 0.09

b. 0.5

c. 2.73

d. 20

7. From what distribution is this test statistic?

a. N(0, 1)

b. N(1420, 7.30)

c. t distribution with 29 degrees of freedom

d. t distribution with 28 degrees of freedom

8.) The p-value for this test is 0.005. Which of the following is a proper interpretation of this p- value?

a.There is a 0.5% chance that the null hypothesis is true.

b. If the population mean SAT score really is 1420, there's a 0.5% chance that the sample a. mean SAT score from 30 statistics majors would equal 1440.

c.If the population mean SAT score really is 1420, there's a 0.5% chance that the sample mean SAT score from 30 statistics majors would be 1440 or lower.

d. If the population mean SAT score really is 1420, there's a 0.5% chance that the sample mean SAT score from 30 statistics majors would be 1440 or higher.

beigeserval271

Never forget that even small effects can be statistically significant if the samples are large. During a three-year period, 8 of the 57 headed by men and 6 of the 35 headed by women failed.

(a) Find the proportions of failures for businesses headed by women and businesses headed by men. These sample proportions are quite close to each other. Give the p-value for the hypothesis that the same proportion of women's and men's businesses fail. (Use two-sided alternative). What can we conclude (use alpha as 0.05)?

The p-value was ___________ so we conclude that ____________.

(b) Now suppose that the same sample proportion came from a sample 30 times as large. That is 180 out of 1050 businesses headed by women and 240 out of 1710 businesses headed by men fail. Verify that the proportions of failures are exactly the same as in part (a). Repeat the test for the new data. What can we conclude?

The p-value was ___________ so we conclude that ____________.

c) It is wise to use a confidence interval to estimate the size of an effect rather than just giving a p-value. Give 95% confidence intervals for the difference between proportions of men's and women's businesses that fail for the settings of both (a) and (b).

Interval for smaller samples: ___________ to ___________.

Interval for larger samples: ___________ to ___________.

What is the effect of larger samples on the confidence interval?

viridiancoyote964

STAB22H3 Chapter Notes - Chapter 18 - 20: Null Hypothesis, Alternative Hypothesis, Confidence Interval

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