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Lab Activity 7: Hypothesis Testing for Proportions and Means: A Comprehensive Analysis Using Statistical Methods

Lab assignment covering hypothesis testing for proportions and means with statistical methods.

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    Lab Activity 7 1 Lab Activity 7 Hypothesis Testing Data Set: SPX Monthly Number of Questions: 4 P - value Guidelines when using Standard Normal Table (i.e. the Z - table): Keep this in mind: The method for finding the p - value is based on the alternative hypothesis. Minitab will provide a p - value but if we need to calculate it by hand , we would use the Standard Normal Table and observe the following: i. For Ha: p < p o, then the p - value = P( Z ≤ z) ii. For Ha: p > p o, then the p - value = P( Z ≥ z) iii. For Ha: p ≠ p o , then the p - value = 2P(Z ≥ |z|) That is, find 1 – P(Z < |z|) and then multiply this p - value by 2. 1. Hypothesis Testing for a Proportion – Example 1 Using Software No dataset is needed. Prior to the start of a S tat200 course , a survey was taken to find out students’ level of excitement for the course. It is generally believed that 40% of all World Campus students are excited to take elementary statistics. That means, the null hypothesis is that the percentage of World Campus students excited to take elementary statistics, which was measured by a “3” on the survey, is 0.40 (40%). The alternative hypothesis is that true percentage is less than 0.40 (40%). a. In this case, p = true population proportion of World Campus students who are excited to take elementary statistics, measured by a “3” on the survey. Write the null and alternative hypotheses using statistical notation. Hint: Remember that hypotheses are always written about the population . Be sure to use notation for the correct population parameter (should we use notation for a mean or a proportion?) ! iv. Null Hypothesis: H 0 : P=0.40 v. Alternative Hypothesis: H a : P<0.40 b. The survey for Stat200 polled 32 students, of which 10 responded that they are excited to take the elementary statistics course. What is the value of 𝑝 ̂ = percentage of students answering “3” in the sample ? Round your answer to 4 decimal places. 𝑝 ̂ = percentage of students answering “3” in the sample is 10/32=0.3125 c. How does 𝑝 ̂ in part (b) compare to the true population proportion of 0.40? Sample proportion 0.3125 is really less than the population proportion 0.40 .

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    Lab Activity 7 2 d. Use software to perform a hypothesis test for a proportion. Note that in this case, we do not have a data set to follow. Instead, what we have is called “summarized data,” in other words, a count of the final values. Following the written and video instructions in the online notes for “ Using Software to Perform a Summarized One Proportion Test Analysis ,” use software to test the hypotheses in part (a). This is different from the instructions for the case of “raw data!” Copy and paste the output. Test and CI for One Proportion Test of p = 0.4 vs p < 0.4 95% Upper Sample X N Sample p Bound Z - Value P - Value 1 10 32 0.312500 0.447276 - 1.01 0.156 e. What value is given for the test statistic Z in the output? Z= - 1.01 f. What is the p - value? P - value=0.156 g. One way to determine statistical significance is by using a p - value. We compare the p - value to a pre - determined significance level, α . In general, a significance level of 0.05 is used. vi. If the p - value is less than the significance level (0.05), we reject the null hypothesis. This means, we do not have enough evidence to claim the null hypothesis is true. vii. If the p - value is greater than the significance level (0.05), we fail to reject the null hypothesis. This means we do not have enough evidence to support the alternative hypothesis. Based on the p - value in part (f), do we “reject the null hypothesis” or “fail to reject the null hypothesis?” Explain why. We fail to reject the null hypothesis because the p value corresponding to z= - 1.01 is 0.156 which is greater than 0.05 at 5% level of significance therefore we accept the null hypothesis. h. In real world terms (terms of the problem), write a conclusion about the proportion of World Campus students who are excited to take elementary statistics. The conclusion is that the proportion of the sample who is excited is equal to 0.40 the proportion of World Campus students to take the elementary statistics. i. Suppose the study intended to find out if more than 40% of World Campus students are excited

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