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- A study of parental empathy for sensitivity cues and baby temperament (higher scores mean more empathy) was performed. Let x, be a random variable that represents the score of a mother on an empathy test (as regards her baby). Let x, be the empathy score of a father. A random sample of 35 mothers gave a sample mean of x, = 69.38. Another random sample of 34 fathers gave x, = 57.34. Assume that o, = 11.27 and o, = 11.17. (a) Let u, be the population mean of x, and let u, be the population mean of x,. Find a 99% confidence interval for u, - µz. (Round your answers to two decimal places.) lower limit upper limit (b) Examine the confidence interval and explain what it means in the context of this problem. Does the confidence interval contain all positive, all negative, or both positive and negative numbers? What does this tell you about the relationship between average empathy scores for mothers compared with those for fathers at the 99% confidence level? O Because the interval contains…A medical researcher is interested in determining if there is a relationship between adults over 50 who exercise regularly and levels of blood pressure. A random sample of 236 adults over 50 is selected and the results are given below. Calculate the test statistic to test the claim that regular exercise and blood pressure are independent. Use α = 0.01.Two separate samples receive two different treatments. The first treatment group (N = 9) has a mean of 50 with SS = 710. The second treatment group (N = 6) has a mean of 60 with SS = 460. Is the second treatment group significantly larger than the first? What is the effect size?
- You are testing the null hypothesis that there is no linear relationship between two variables, X and Y. From your sample of n= 18, you determine that b, = 5.1 and Sp, =1.3. a. What is the value of tSTAT? b. At the a = 0.05 level of significance, what are the critical values? c. Based on your answers to (a) and (b)., what statistical decision should you make? d. Construct a 95% confidence interval estimate of the population slope, P, hat are the hypotheses to test? H, B, #0 H, P, =0 H P, s0 H, B, >0 H, B, 20 H, P, <0 H B, =0 H, P, +0 ISTAT = Round to two decimal places as needed) b. The lower critical value is The upper critical value is (Round to four decimal places as needed.) c. What statistical decision should you make?The following data show the pattern of results that was obtained in a study by Liguori and Robinson (2001) examining how different levels of alcohol and caffeine consumption influenced response time in a simulated driving test. The means show the average response time in milliseconds for different combinations of alcohol and caffeine. Remember larger reaction time means someone is slower to respond. For these data, indicate which are true/false There is an interaction, caffeine has a larger impact on reaction times (makes people respond faster) when participants haven’t had alcohol) A. True B. FalseSolid fats are more likely to raise blood cholesterol levels than liquid fats. Suppose a nutritionist analyzed the percentage of saturated fat for a sample of 6 brands of stick margarine (solid fat) and for a sample of 6 brands of liquid margarine and obtained the following results: Stick:[25.5,26.7,26.5,26.6,26.3,26.4] Liquid:[16.5,17.1,17.5,17.3,17.2,16.7] We want to determine if there a significant difference in the average amount of saturated fat in solid and liquid fats. What is the test statistic? a) z = 39.604 b) t = 25.263 c) t = 39.604 d) z = 39.104 e) t = 39.104
- A study was conducted to determine if lung cancer altered levels of surfactant in the alveoli of the lung. Seven healthy subjects in the study yielded the following data on surfactant levels: 18, 12, 15, 15, 16, 9, 17. Seven lung cancer patients yielded the following results: 16, 8, 7, 15, 11, 12, 9. Do these data indicate a difference in the surfactant level with cancer? Let α = 0.05. Give the p-value.The authors of a paper classified characters who were depicted smoking in movies released between a certain range of years. The smoking characters were classified according to sex and whether the character type was positive, negative, or neutral. The resulting data are summarized in the accompanying table. Assume that it is reasonable to consider this sample of smoking movie characters as representative of smoking movie characters. Do the data provide evidence an association between sex and character type for movie characters who smoke? Use α = 0.05. Sex = Male Female Positive Negative Neutral 256 Character Type 85 107 11 132 51 Calculate the test statistic. (Round your answer to two decimal places.) x² Use technology to calculate the P-value. (Round your answer to four decimal places.) P-value = What can you conclude? O Reject Ho. There is convincing evidence to conclude that there is an association between sex and character type for movie characters who smoke. Fail to reject Ho.…In the US, 42.3% of all people have type O blood, 40.8% have type A blood, 12% have type B blood and 4.9% have type AB blood. A researcher wants to see if the distribution of blood type is different for millionaires. The table below shows the results of a random sample of 897 millionaires. What can be concluded at the significant level of a = 0.1. For this study, we should use [x²GOF-Test Your friend Henry helped you with the null and alternative hypotheses... Ho: The distributions of blood types are the same between the general population and the millionaires. H₁: The distributions of blood types are NOT the same between the general population and the millionaires. You drew 897 samples, and the observed frequencies are recorded below. Please complete the table (round answers to at least 4 decimal places). Blood Type 0 A B AB Observed Frequency 375 The degree of freedom = 366 104 52 The test-statistic for this data = The p-value for this sample= Expected Frequency (Please show your…
- What are the independent and dependent variables for the following examples? What statistical test would you use for each of the following scenarios? What would you set your alpha-level at? Sally wants to examine whether there is a difference in muscular strength between participants who engaged in an 8-week resistance training program and participants who engaged in an 8-week endurance training program. The participants only took part in one of the 8-week programs, not both. What test would she use to determine whether the differences in muscular strength are significant? Why?A researcher wanted to examine whether type of dog food (freeze dried meat vs generic brand kibble) would affect dogs’ attention span. The researcher hypothesized that dogs who ate freeze dried meat would have longer attention spans than those who ate generic brand kibble. The researcher used a single sample of 13 subjects, that took part in both treatment conditions. The researcher set the alpha level at .01. The mean of the difference scores (MD)was 7.0 and the SSD for the difference in attention spans was 144. What is the calculated test statistic to the nearest thousandth? Be sure to put the positive or negative sign in front of it. Note: SHOW ALL WORK!!! Based on your work above, do you reject or retain the null? reject retain Based on your conclusion regarding the null, was there a treatment effect? Yes NoAccording to a certain government agency for a large country, the proportion of fatal traffic accidents in the country in which the driver had a positive blood alcohol concentration (BAC) is 0.34. Suppose a random sample of 109 traffic fatalities in a certain region results in 50 that involved a positive BAC. Does the sample evidence suggest that the region has a higher proportion of traffic fatalities involving a positive BAC than the country at the x = 0.01 level of significance? Because npo (1-Po) = 24.5 > 10, the sample size is (Round to one decimal place as needed.) What are the null and alternative hypotheses? p = 0.34 versus H₁: p > 0.34 Ho: p (Type integers or decimals. Do not round.) Find the test statistic, Zo. Zo = 2.62 (Round to two decimal places as needed.) Find the P-value. P-value = (Round to three decimal places as needed.) less than 5% of the population size, and the sample is given to be random, the requirements for testing the hypothesis are satisfied.