question 23\n0 / 3 points\na company claims that the average battery life of its smartphones is at least 10…

question 23\n0 / 3 points\na company claims that the average battery life of its smartphones is at least 10 hours ($h_0:mugeq10$). a sample of 16 phones has a mean battery life of 9.5 hours with a sample standard deviation of 1.2 hours. calculate the t - statistic for this hypothesis test. round to two decimal places. 1.667 × (-1.67)\nquestion 24\n0 / 3 points\na company tests two website layouts. on layout a, 100 out of 500 visitors made a purchase. on layout b, 140 out of 600 visitors made a purchase. calculate the test statistic ($z_c$) for a hypothesis test comparing the two proportions. round to two decimal places. - 1.33 × (-1.14)\nquestion 26\n0 / 3 points\nthe time required to complete a task is normally distributed with a mean of $mu = 50$ minutes and a standard deviation of $sigma = 8$ minutes. what is the probability that a randomly selected task takes between 40 and 55 minutes? round to four decimal places. 0.6284 × (0.6288)\nquestion 27\n0 / 3 points\na sample of 25 employees has a mean salary of $65,000 with a sample standard deviation of $8,000. calculate the 95% confidence interval for the true mean salary. (the critical t - value for df = 24 is 2.064). round to the nearest dollar and write the answer in the following format: (00000, 00000) 68302 × ((61698, 68302))\nquestion 29\n0 / 3 points

Answer

Question 23

Explanation:

Step1: Recall t - statistic formula

$t=\frac{\bar{x}-\mu}{\frac{s}{\sqrt{n}}}$

Step2: Identify values

$\bar{x} = 9.5$, $\mu = 10$, $s = 1.2$, $n = 16$

Step3: Substitute values

$t=\frac{9.5 - 10}{\frac{1.2}{\sqrt{16}}}=\frac{- 0.5}{\frac{1.2}{4}}=\frac{-0.5}{0.3}\approx - 1.67$

Answer:

$-1.67$

Question 24

Explanation:

Step1: Calculate sample proportions

$p_1=\frac{100}{500}=0.2$, $p_2=\frac{140}{600}\approx0.2333$, $n_1 = 500$, $n_2=600$

Step2: Calculate pooled proportion

$p=\frac{100 + 140}{500+600}=\frac{240}{1100}\approx0.2182$

Step3: Recall z - statistic formula for two proportions

$z_c=\frac{p_1 - p_2}{\sqrt{p(1 - p)(\frac{1}{n_1}+\frac{1}{n_2})}}$

Step4: Substitute values

$z_c=\frac{0.2-0.2333}{\sqrt{0.2182\times(1 - 0.2182)\times(\frac{1}{500}+\frac{1}{600})}}\approx - 1.14$

Answer:

$-1.14$

Question 26

Explanation:

Step1: Calculate z - scores

$z_1=\frac{40 - 50}{8}=\frac{-10}{8}=-1.25$, $z_2=\frac{55 - 50}{8}=\frac{5}{8}=0.625$

Step2: Use z - table

$P(-1.25<Z<0.625)=P(Z < 0.625)-P(Z<-1.25)$ $P(Z < 0.625)=0.7340$, $P(Z<-1.25)=0.1056$ $P(-1.25<Z<0.625)=0.7340 - 0.1056=0.6284$

Answer:

$0.6284$

Question 27

Explanation:

Step1: Recall confidence - interval formula

$\bar{x}\pm t_{\alpha/2}\frac{s}{\sqrt{n}}$

Step2: Identify values

$\bar{x}=65000$, $t_{\alpha/2}=2.064$, $s = 8000$, $n = 25$

Step3: Calculate margin of error

$E=t_{\alpha/2}\frac{s}{\sqrt{n}}=2.064\times\frac{8000}{\sqrt{25}}=2.064\times1600 = 3302.4$

Step4: Calculate confidence interval

Lower limit: $65000-3302.4 = 61697.6\approx61698$ Upper limit: $65000 + 3302.4=68302.4\approx68302$

Answer:

$(61698,68302)$