Question

The following data represent the pH of rain for a random sample of 12 rain dates. a normal probability plot suggest the data could come from a population that is normally distributed. a boxplot indicates there are no outline. complete part A through d.
a)determine a point estimate for the population mean. 5.20, 5.02, 4.87, 5.72, 4.57, 4.76, 4.99, 4.74, 4.56, 4.80, 5.19, 4.68
b)construct and Interpret a 95% confidence interval for the mean pH of rainwater. select the correct choice below and fill in the answer boxes to complete your choice.
A) if repeated samoles are taken, 95% of them will have a sample pH of rain water between [ ] & [ ].
B)there is a 95% chance that the true mean pH of rain water is between [ ] & [ ].
C) there is 95% confidence that the population mean pH of rain water is between [ ] & [ ].
c) construct and interpret a 99% confidence interval for the mean pH of rainwater. Select the correct Choice below and fill in answer boxes to complete your choice.
A)there is 99% confidence that the population mean pH of rain water is between [ ] & [ ].
B)there is a 99% chance that the true mean pH of rain water is between [ ] & [ ].
C)if repeated samoles are taken, 99% of them will have a sample pH of rain water between [ ] & [ ].
d) what happens to the interval as the level of confidence is changed? Explain why is a logical result.
-As the level of confidence increases l, the width of the interval[ increases, decreases] this makes sense since the [ point estimate, sample size, margin of error] [decreases, increases]

Answer 1

Answer:

Step-by-step explanation:

a) Estimate for population mean = Sum/n =$\frac{59.1}{12} =4.925$

b) Variance = 0.099208

Std dev = 0.314974

Std error = 0.0950

For 95% margin of error = 1.96*Std error

=0.1861

Confidence interval = $(4.925-0.1861, 4.925+0.1861)\\=(4.7389, 5.1111)$

Interpretation of confidence interval:

A) if repeated samoles are taken, 95% of them will have a sample pH of rain water between [ ] & [ ].

For 99%  CI,  z value = 2.59

Conf interval = (4.6790, 5.1710)

C)if repeated samoles are taken, 99% of them will have a sample pH of rain water between [ ] & [ ].

As the level of confidence increases l, the width of the interval[ increases] this makes sense since the [  margin of error] [increases]

Answer 2

a) Estimate for population mean

$=\dfrac{sum\; of\; all\; observations}{number \;of\;all\;observations}=\dfrac{59.1}{12}=4.925$

Variance $= 0.099208$ , Std. dev $= 0.314974$  and Std. error $= 0.0950$

For $95$ % margin of error $=1.96*Std. error=0.1861$

Confidence interval $=(4.925-0.1861,4.925+0.1861)=(4.7389,5.1111)$

Interpretation of confidence interval:

A) If repeated samples are taken, $95$% of them will have a sample pH of rain water between [ ] & [ ].  

Confidence interval $=(4.7389,5.1111)$

C)if repeated samples are taken, $99$% of them will have a sample pH of rain water between [ ] & [ ].

For $99$%  CI,  $Z$ value $= 2.59$

Confidence interval $= (4.6790, 5.1710)$

As the level of confidence increases, the width of the interval[ increases] this makes sense since the margin of error [increases].

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