Use technology to help you test the claim about the population​ mean, μ​, at the given level of​ significance, α​, using the given sample statistics. Assume the population is normally distributed.   ​Claim: μ>1290​; α=0.05​; σ=206.11. Sample​ statistics: x=1305.71​, n=250       Identify the null and alternative hypotheses. Choose the correct answer below.     A. H0​: μ≤1290 Ha​: μ>1290   B. H0​: μ>1290 Ha​: μ≤1290   C. H0​: μ≥1290 Ha​: μ<1290   D. H0​: μ>1305.71 Ha​: μ≤1305.71   E. H0​: μ≤1305.71 Ha​: μ>1305.71   F. H0​: μ≥1305.71 Ha​: μ<1305.71 Calculate the standardized test statistic.   The standardized test statistic is enter your response here. ​(Round to two decimal places as​ needed.) Determine the​ P-value.   P=enter your response here ​(Round to three decimal places as​ needed.) Determine the outcome and conclusion of the test.   ▼   Fail to reject Reject H0. At the 5​% significance​ level, there ▼   is is not enough evidence to ▼   support reject the claim.

In the population of senior students at Shermer High School, the proportion who plan to attend college is 0.64. In a random sample of 100 students from this population, the proportion who plan to attend college is 0.75.  We would call the value 0.64 a   P-value. z-score. parameter statistic significance level.

You are performing a two-tailed significance test on a proportion and you calculate z-value of2.43. The p-value isa. 0.00375b. 0.0075c. 0.0150d. 0.9925e. 0.9963

Statistics students believe that the mean score on a first statistics test is 65. The instructor thinks that the mean score is higher. She samples 10 statistics students and obtains the scores: Grades 69 69 63.9 68.4 62.7 73.5 73.5 64.3 Test grades are believed to be normally distributed. Use a significance level of 5%. A. State the alternative hypothesis: HA: Ομ 65 B. State the mean of the sample: C. State the standard error of the sample means: D. State the test statistic: t = E. State the p-value: F. Decision: O Fail to reject the null hypothesis. Reject the null hypothesis. 73.5 96

Statistics students believe that the mean score on a first statistics test is 65. The instructor thinks that the mean score is higher. She samples 10 statistics students and obtains the scores: Grades 74.4 96 83.2 65 63.9 64.3 74.4 69 68.4 88 Test grades are believed to be normally distributed.Use a significance level of 5%. State the alternative hypothesis: HA:HA: μ>65μ>65 μ<65μ<65 μ≠65μ≠65 State the mean of the sample:  (Round to two decimal places.) State the standard error of the sample means:  (Round to four decimal places.) State the test statistic: t=t=  (Round to four decimal places.) State the p-value:  (Round to four decimal places.) Decision: Reject the null hypothesis. Do not reject the null hypothesis.

The US Department of Energy reported that 48% of homes were heated by natural gas. A random sample of 331 homes in Oregon found that 132 were heated by natural gas. Test the claim that proportion of homes in Oregon that were heated by natural gas is different than what was reported. Use a 1% significance level. Give answer to at least 4 decimal places. What are the correct hypotheses? (Select the correct symbols and use decimal values not percentages.) H0:                   H1:                     Based on the hypotheses, compute the following:Test Statistic = p-value =  Based on the above we choose to       The correct summary would be:       that the proportion of homes in Oregon that were heated by natural gas is different than what the DOE reported value of 48%.

Aspirin III: Decision and Conclusion Regarding the experiment in the data frame Aspirin from the abd package, the researchers wanted to know whether or not taking aspirin affects one's risk of developing cancer. Recall that they defined their parameters as follows: p1 = the proportion of ALL individuals who would develop cancer, if all of them were to take aspirin like the subjects in the Aspirin group did. p2 = the proportion of ALL individuals who would develop cancer, if all of them were to take a placebo, like the subjects in the placebo group did. They ran the code for a two-sided significance test and got the following results: ## ## ## Inferential Procedures for the Difference of Two Proportions p1-p2:##   cancer grouped by treatment ## ## ## Descriptive Results:## ##          yes     n estimated.prop## Aspirin 1438 19934        0.07214## Placebo 1427 19942        0.07156## ## ## Inferential Results:## ## Estimate of p1-p2:    0.0005805 ## SE(p1.hat - p2.hat):  0.002586 ## ##…

8. Hypothesis Test of Equal Variances. Test the given claim. Use a significance level of a = 0.05 and assume that all populations are normally distributed. Claim: IQ scores of statistics students vary less than IQ scores of other students. Statistics students: n = 28, x = 118, s = 10.0 Other students: n = 25, x = 112, s = 12.0

Use the data on student load. to test the claim that mean student load is more than 6.5 units.  Use α = 0.10.  Assume all requirements have been met. Student Unit Load 3, 12, 6, 9, 6, 12, 15, 12, 7, 9, 3   Test the claim that mean student load is more than 6.5 units.  Use α = 0.10.  Assume all requirements have been met.

Random Sample of Length of Eruption at Old Faithful 108 99 105 103 99 106 90 104 109 101 DES 105 106 103 120 108 102 103 110 104 113 100 109 102 100 116 101 111 110 102 105 110 95 107 Source: LaDonna Hansen, Park Curator 103 92 103 110 101 104 90 101 108 94 110