Question

two seperate questions

The histogram below shows the distances (in meters) of all qualifying throws for the women's javelin event at the 2004 Summer Olympics Which of the following terms apply to this histogram? (Select all that apply.) bimodal symmetric unimodal positively skewed uniform negatively skewed You wish to test the following claim (H) at a significance level of a = 0.001. H : 1 = 2 H:1 + 12 You believe both populations are normally distributed, but you do not know the standard deviations for either. Assume you should use a non-pooled test. You obtain the following two samples of data. Sample #1 Sample #2 103 97.9 74.3 100 91.2 100 92.2 71.5 96.4 96.4 82.2 97.3 93.4 75.3 92. 2 9 1. 4 78.2 86.5 87.7 93.8 116.6 94. 6 76.3 100.5 69.4 98.9 88.4 99.1 104.8 84.4 94.3 91.4 81.4 88.2 89.8 94.6 97. 4 74.8 93.4 103.8 103.8 78.1 78.5 What is the critical value for this test? For this calculation, use the degrees of freedom reported from the technology you are using. (Report answer accurate to three decimal places.) critical value =

Answer 1

Unimodal (This histogram shows that the distribution has only one mode. The interval that has the highest frequency contains mode. height of each bar represents the frequency of that interval.)
Negatively skewed (Negatively Skewned means when the tail on the left side of the distribution is longer or fatter. The mean and median will be greater than the mode.)

In this problem we will use 2 sample t test (since population s.d not known)
Also we are to use non-pooled test. t test statistics for non-pooled is:
$\boldsymbol{t=\frac{\bar{x}_1-\bar{x}_2}{s_p \sqrt{\frac{1}{n_1}+\frac{1}{n_2}}}}$
with degreeg of freedom v, v is
  $\boldsymbol{v=\frac{(\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2})^2}{\frac{1}{n_1-1} (\frac{s_1^2}{n_1})^2 + \frac{1}{n_2-1} (\frac{s_2^2}{n_2})^2}}$
Here si sd for sample i and ni is the sample size of i th sample
Formula for sample sd is
$\boldsymbol{s=\sqrt{\frac{\sum_{i=1}^{n}(x_i-\bar{x})}{n}}}$
Hence s1= 11.75362 n1=24 s2= 8.330831 n2=19
$\boldsymbol{Hence\;\; DF\; (v)\; =\;40.5748\approx 40}$
Critical value of t=
740.0005) = 3.551