data: Height by Sex t = -7.9007, df = 41, p-value = 4.546e-10 alternative hypothesis: true difference in means between group F and group M is less than 0 99 percent confidence interval: -Inf -4.806541 sample estimates: mean in group F mean in group M 64.64706 71.57692
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546e-10, which is less than 0.01. Therefore, we reject the null hypothesis. Show more…
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Shaiju T.
The average adult male height in a certain country is 170 cm. We suspect that the men in a certain city in that country might have a greater average height due to some environmental factors. We pick a random sample of size 9 from the adult males in the city and obtain the following values for their heights (in cm): 176.2, 157.9, 160.1, 180.9, 165.1, 167.2, 162.9, 155.7, 166.2. Assume that the height distribution in this population is normally distributed. We need to decide between H0: μ = 170 and H1: μ > 170. Based on the observed data, is there enough evidence to reject H0 at significance level α = 0.05? Fill the blanks and explain how you got each answer. a) x̄: __________ b) sₓ: __________ c) SE( x̄ ): __________ d) test statistic: tₓ: __________ e) P-value: __________ f) Compare P-value with α: __________ g) Conclusions:
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1. In 1990, the mean height of women 20 years of age or older was 63.7 inches based on data obtained from the CDC. Suppose that a random sample of 45 women who are 20 years of age or older in 2015 results in a mean height of 63.9 inches with a standard deviation of 0.5 inch. Does your sample provide sufficient evidence that women today are taller than in 1990? Perform the appropriate test at the 0.05 level of significance. (a) Give the appropriate hypotheses for this test and define any parameters used. (b) List and verify conditions for the appropriate hypothesis test. (c) Give the appropriate test statistic. Show formula, work, and value. (d) Find the rejection region. Draw an appropriate picture, show work. (e) What is your decision regarding the null hypothesis? (f) What are your conclusions about this particular test?
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