STA-1013 Lecture Notes - Lecture 11: Standard Score, Statistical Hypothesis Testing, Null Hypothesis

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15 Nov 2016

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One-tailed hypothesis tests: finding the standard score. Since the sampling distribution is a normal distribution, the standard score of the sample mean represents a quantitative measure of the distance between the sample mean and the claimed population mean. Computing the standard score for the sample mean in a hypothesis test: standard deviation for the distribution of sample means= , standard score for the sample mean: z=(cid:3029)(cid:3028) distribution. Z= sample mean-population mean/ standard deviation of sampling. A two-tailed test is significant at the 0. 05 level if the standard score of the sample mean is at or below the critical value of -1. 96 or at or above a critical value of 1. 96. For significance at the 0. 01 level, the critical values are -2. 575 and 2. 575: p-values. To find the p-value for a sample mean in a two-tailed test, first use the standard score of the sample mean to find the p-value assuming the test is one-tailed.

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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

6. As the test statistic becomes larger, the p-value

(a) gets smaller

(b) becomes larger

(d) becomes negative.

7. To describe the sampling distribution of the sample proportion, we use

(a) The sample proportion

(b) The population proportion

(d) The population mean

8. When small samples are used to estimate a population mean, in cases where the population standard deviation is unknown and the original distribution is normal:

(a) There always will be a large amount of sampling error.

(b) the t-distribution must be used to obtain the critical value.

(d) the z distribution must be used to obtain the critical value.

periwinkleyellowjacket100

A sample of 36 observations is selected from a normal population. The sample mean is 12, and the population standard deviation is 3. Conduct the following test of hypothesis using the 0.01 significance level: H0: μ ≤ 10 H1: μ > 10

a. Is this a one- or two-tailed test?

b. What is the decision rule, Reject H0 when Z > 2.33 or when Z <= 2.33 ?

c. What is the value of the test statistic? (Round the final answer to 1 decimal place.)

d. What is your decision regarding H0? (Reject or Accept) ?

e. What is the p-value, one, zero, or close to zero ?

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STA-1013 Lecture Notes - Lecture 11: Standard Score, Statistical Hypothesis Testing, Null Hypothesis

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