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In a sample of 10 randomly selected women, it was found that their mean height was 63.4 inches. From previous studies, it is assumed that the standard deviation is 2.4 inches and that the population of height measurements is normally distributed. Round to three decimal places. Construct the 99% confidence interval for the population mean height of women: What is the point estimate? What is the critical value? What is the margin of error? The interval is from am % confident that the true population mean height of women is between and b) If the sample size was doubled to 20 women, what will be the effect on the confidence interval? An increase in the sample size will the width of the confidence interval: Provide an appropriate response.
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A Statistics class is estimating the mean height of all female students at their college. They collect a random sample of 36 female students and measure their heights. The mean of the sample is 65.3 inches. The standard deviation is 5.2 inches. What is the 90% confidence interval for the mean height of all female students in their school? Assume that the distribution of individual female heights at this school is approximately normal. A. (56.5, 74.1) B. (63.6, 67.0) C. (63.8, 66.8) D. (63.9, 66.7)
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Adult male height is assumed to be normally distributed with a mean of 175.5 cm within the population. A sample of 26 college students was recruited to have their heights measured, and the mean height was 182 cm, with a standard deviation of 17 cm. Researchers want to know if the collected sample has a height that is significantly different from that of the population mean. Use 2 decimal points for all your calculations. Using a significance level of 0.01, answer the following questions. (a) What type of statistical test should the researchers conduct? Why? (1 mark) (b) State the hypotheses for this scenario. (1 mark) (c) Conduct a hypothesis test based on question 1a) to determine what the researcher should conclude from this study. Write your decision using the critical value method and confidence interval method. Relate it to the research question. (2 marks)
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