Mathematics, 18.08.2020 18:01, kelenski4

You measure 46 watermelons' weights, and find they have a mean weight of 60 ounces. Assume the population standard deviation is 8.5 ounces. Based on this, construct a 99% confidence interval for the true population mean watermelon weight. Give your answers as decimals, to two places.

Answers: 3

Show answers

Answers

answered: levon15

A 99% confidence for the true population mean watermelon weight is [56.77 ounces, 63.23 ounces] .

Step-by-step explanation:

We are given that you measure 46 watermelons' weights, and find they have a mean weight of 60 ounces.

Assume the population standard deviation is 8.5 ounces.

Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;

P.Q. = $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{} n} }$ ~ N(0,1)

where, $\bar X$ = sample mean weight = 60 ounces

$\sigma$ = population standard deviation = 8.5 ounces

n = sample of watermelons = 46

$\mu$ = population mean watermelon weight

Here for constructing a 99% confidence interval we have used a One-sample z-test statistics because we know about the population standard deviation.

So, 99% confidence interval for the population mean, $\mu$ is ;

P(-2.58 < N(0,1) < 2.58) = 0.99 {As the critical value of z at 0.5% level

of significance are -2.58 & 2.58}

P(-2.58 < $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{} n} }$ < 2.58) = 0.99

P( $-2.58 \times {\frac{\sigma}{\sqrt{} n} }$ < ${\bar X-\mu}$ < $2.58 \times {\frac{\sigma}{\sqrt{} n} }$ ) = 0.99

P( $\bar X-2.58 \times {\frac{\sigma}{\sqrt{} n} }$ < $\mu$ < $\bar X+2.58 \times {\frac{\sigma}{\sqrt{} n} }$ ) = 0.99

99% confidence interval for $\mu$ = [ $\bar X-2.58 \times {\frac{\sigma}{\sqrt{} n} }$ , $\bar X+2.58 \times {\frac{\sigma}{\sqrt{} n} }$ ]

= [ $60-2.58 \times {\frac{8.5}{\sqrt{46} } }$ , $60+2.58 \times {\frac{8.5}{\sqrt{46} } }$ ]

= [56.77 ounces, 63.23 ounces]

Therefore, a 99% confidence for the true population mean watermelon weight is [56.77 ounces, 63.23 ounces] .

answered: Guest

that is the sum

step-by-step explanation:

there are no other answers without knowing the variables values

answered: Guest

"it's not the heat, it's the humidity". that's a partly valid phrase you may have heard in the summer, but it's actually both. the heat index, also known as the apparent temperature, is what the temperature feels like to the human body when relative humidity is combined with the air temperature. this has important considerations for the human body's comfort. when the body gets too hot, it begins to perspire or sweat to cool itself off. if the perspiration is not able to evaporate, the body cannot regulate its temperature. evaporation is a cooling process. when perspiration is evaporated off the body, it effectively reduces the body's temperature. when the atmospheric moisture content (i.e. relative humidity) is high, the rate of perspiration from the body decreases. in other words, the human body feels warmer in humid conditions. the opposite is true when the relative humidity decreases because the rate of perspiration increases. the body actually feels cooler in arid conditions. there is direct relationship between the air temperature and relative humidity and the heat index, meaning as the air temperature and relative humidity increase (decrease), the heat index increases (decreases).

step-by-step explanation: