Researchers are interested in estimating the prevalence of illegal drug use among teenagers aged 13-17. A recent national survey has estimated the population prevalence for illegal drug use in this demographic is 40%. The research team has pooled together 55 teenagers in this age range and determined that 10 use illegal drugs. Can we assume a normal approximation is possible in this instance?

Retinitis pigmentosa (RP) is a hereditary ocular diseasein which patches of pigment appear on the retina, potentially resulting in substantial vision loss and in somecases complete blindness. An important issue is how fastthe subjects decline. Visual field is an important measureof area of vision, which is measured in degree2. A visualfield area for a normal person is around 11,000 degree2.The longitudinal data in Table 11.29 were provided by anindividual patient.Table 11.29         Longitudinal visual field data forone RP patientTime Visual field area lnVisit (yr) (degree2) (visual field area)1 0 3059 8.032 1 3053 8.023 2 1418 7.264 3 1692 7.435 4 1978 7.596 5 1567 7.367 6 1919 7.568 7 1998 7.609 11 1648 7.4110 13 1721 7.4511 15 1264 7.14mean 6.09 1938 7.532sd 4.97 597 0.280Suppose the rate of change of ln (visual field) is a linearfunction of follow-up time.11.103 Write down a linear regression model that summarizes this relationship.

Miss America winners from the 1920's and 1930's had a average BMI of 19.4. A sample of recent winners had reported BMIs of 18.7, 18.7, 18.5, 19.2, 19.3, 18.7, 18.6, 19.8, 19, 19.6, and 19 . Do recent winners appear to be significantly different from those in the 1920s and 1930s? (assume normality). Show all the steps of a hypothesis.

You perform an ANOVA test comparing average height among patients at a hospital according to whether they were born in the 1950s, 1960s, or 1970s. The results from the test are significant at the level of 0.05. What can you conclude from this test?       You can reject the null hypothesis that the data comes from a sample where mMean heights are not different according to decade of birth, but you can not determine which decades are different from each other.      Mean heights for each decade of birth are different from each other.      The mean height of those born in 1970 is more than the other groups.      The mean height of those born in 1950 is more than the other groups.

Please show all work/steps

part 3

Please provide only typed answer solution no handwritten solution needed allowed

A random sample of 76 eighth-grade​ students' scores on a national mathematics assessment test has a mean score of 273. This test result prompts a state school administrator to declare that the mean score for the​ state's eighth graders on this exam is more than 270. Assume that the population standard deviation is 33. At α=0.02​, is there enough evidence to support the​ administrator's claim? Complete parts​ (a) through​ (e). Part 1 ​(a) Write the claim mathematically and identify H0 and Ha. Choose the correct answer below.   A.) H0​: μ≥270 (claim)       Ha​: μ<270   B.) H0​: μ≤270 (claim)       Ha​: μ>270   C.) H0​: μ=270 (claim)       Ha​: μ>270   D.) H0​:μ≤270       Ha​: μ>270 ​(claim)   E.) H0​: μ<270       Ha​: μ≥270 ​(claim)   F.) H0​: μ=270      Ha​: μ>270 (claim)     (b) Find the standardized z, and its coresponding area      z=_____   (c) Find the P-value P-value =_____   (d) Decide whether to reject or fail the null…

1. Describe the key features of the normal curve and explain why the normal curve in real-life distributions nevermatches the model perfectly.

Ride services are on the rise, such as Uber and Lyft. You wondered if the recent news reports of crime occurring with these ride services impacted the usage of them, especially with women. You decide to conduct  a survey about ride service usage among male and female college students. The results showed that 19 males use ride services and 11 do not. While 12 females use ride services and 18 do not. Calculate the chi-square statistic: