The Whitcomb Company manufactures a metal ring for industrial engines that usually weighs about 50 ounces. A random sample of 50

Answer:

a) Null hypothesis:    

Alternative hypothesis:  

b)   (1)  

Where  

c)    

d) In this scenario, we notice that thus the conclusion for this case would indicate

Step-by-step explanation:

Information provided

denote the number of men possessing smartphones  

signify the number of women possessing smartphones

group of men sampled

group of women sampled

symbolize the proportion of men with smartphones

symbolize the proportion of women with smartphones

denote the pooled estimate of p

z would denote the test statistic

signify the value

Part a

The objective is to evaluate if there is a disparity in smartphone ownership between men and women; the hypothesis statements would be:  

Null hypothesis:    

Alternative hypothesis:    

Part b

The statistic relevant to this case is expressed as:

  (1)  

Where  

Part c

By substituting the provided information, we find:

Part d

In this instance, it is evident that thus the conclusion for this case would seem

Answer: (97.98, 112.020)

Step-by-step explanation: We will create a 95% confidence interval for the average weight of melons.

Given the information, we determine that the critical value for the interval needs to be retrieved from a t distribution table due to the sample size being below 30 (specifically, 20), and we are provided with the sample standard deviation (s = 15 lb).

The parameters provided are:

Sample mean = x = 105 lb

Sample standard deviation = s = 15 lb

Sample size = n = 20

To establish the 95% confidence interval, we indicate that the level of significance is 5%.

The formula for the confidence interval is:

u = x + tα/2 × s/√n... for the upper limit

u = x - tα/2 × s/√n... for the lower limit.

tα/2 represents the critical value for the test (which will be determined using the t distribution table).

To derive tα/2, we look for the value based on the degrees of freedom (sample size - 1) against the significance level for a two-tailed test (α/2 = 0.025%) in a t distribution table.

For the upper limit, we calculate:

u = 105 + 2.093×15/√20

u = 105 + 2.093× (3.3541)

u = 105 + 7.020

u = 112.020.

u = 105 - 2.093×15/√20

u = 105 - 2.093× (3.3541)

u = 105 - 7.020

u = 97.98

Confidence interval (97.98, 112.020)

Answer:

The formula representing the penny's height as a function of time is:

After 7 seconds, the height of the penny will reach 667 feet.

Step-by-step explanation:

The penny experiences free fall.

With an initial velocity of zero and an initial height of h(0)=1,451.

Gravity acts as the acceleration, measured as g=32 ft/s^2.

The model can be initiated by analyzing speed:

Then, the height is expressed as:

The height of the penny at approximately 7 seconds can be calculated as:

After 7 seconds, the penny will stand at a height of 667 feet.