Question

8 pts Question 11 A climate scientist wishes to estimate the mean temperature in Jakarta, Indonesia. The scientist selects a random sample of 30 days, and records the temperature reported for each day, the mean of the sample is 91.3°F, and the sample standard deviation is s = 6.6°F Use this data to construct a 90% confidence interval for the true mean temperature. (88.253, 94.347) (89.253, 93.347) (90253,95.347) (86.253.95.347)

Answer 1

Solution :

Given that,

$\bar x$ = 91.3

s = 6.6

n = 30

Degrees of freedom = df = n - 1 = 25 - 1 = 29

At 90% confidence level the z is ,

$\alpha$ = 1 - 90% = 1 - 0.90 = 0.10

$\alpha$ / 2 = 0.10 / 2 = 0.05

t_{$\alpha$ /2,df} = t_0.05,29 =1.699

Margin of error = E = t_{$\alpha$/2,df} * (s /$\sqrt$n)

= 1.699 * (6.6 / $\sqrt$ 30)

= 2.047

Margin of error = 2.047

The 90% confidence interval estimate of the population mean is,

$\bar x$ - E <$\mu$  < $\bar x$ + E

91.3 - 2.047 < $\mu$ < 91.3 + 2.047

89.253 < $\mu$ < 93.347

(89.253, 93.347)

Option (89.253, 93.347) is correct.