Question

Forty refrigerators from two different models of a refrigerator manufacturer are compared to see if the smaller model uses less energy than the larger model. The energy was measured in kilowatt hours per month (kwh/mo). From years of testing these models, it is known that the standard deviation of kwh/mois 34 kwh/mo for the smaller model and 40 kwh/mo for the larger one. From this survey, the sample means and standard deviations are 125 and 34, and 90 and 40, respectively. If we conduct a hypothesis test, the p-value is 0.0000 O 0.0002 0.0004 O 0.0010 Question 4 1 pts A study is done to determine if baby girls start walking, on average, before baby boys. Fourteen girls and fourteen boys are surveyed. The average ages were 11.4 months for girls with a standard deviation of 0.6 months, and 13.2 months for boys with a standard deviation of 0.7 months. The hypothesis test to use is O two proportions independent group means, population standard deviations unknown O matched or paired samples independent group means. population standard deviations known

Answer 1

Let X₁ and X₂ be the smaller and larger model respectively.

Null hypothesis: $H_0:\mu _1=\mu _2$

Alternate hypothesis:  $H_A:\mu _1<\mu _2$

11
and  
112
are the population mean for the smaller and larger model respectively.

T1 = 125
; $\overline{x_2}=90$ ; $s_1=34$ ; $s_2=40$ ; $n_1=n_2=40$

pooled standard deviation: $s=\sqrt{\frac{(n_1-1)s_1^2+(n_2-1)s_2^2}{n_1+n_2-2}}=37.1214$

test statistic:  $t=\frac{(\overline{x_1}-\overline{x_2})}{s*\sqrt{\frac{1}{n_1}+\frac{1}{n_2}}}=4.22$

degrees of freedom = $n_1+n_2-2=78$

p-value is calculated using p-value(one tailed) calculator by putting the values of the test statistic and degrees of freedom.

p-value =0.000033

p-value is 0.0000

4. independent group means, populations standard deviations unknown.

( Here the two given samples are independent of each other. Sample mean , sample size and sample standard deviation is given ,however population standard deviation is not given)