Answer: Mean = 204.6 , Median = 195 and mode =195
Step-by-step explanation:
The given data for Winona’s bowling scores for the past nine weeks : 195, 180, 195, 212, 208, 231, 179, 246, 195.
The formula to find Mean is given by :-
For median , first we arrange data values in order as
179, 180, 195, 195, 195, 208, 212, 231, 246
Since the number of data values is 9 (odd).
∴ Median = Middle most data value = 195
Also, Mode = Most occurring data value = 195
Answer:
We conclude that a compact microwave oven consumes a mean of more than 250 W.
Step-by-step explanation:
We are given that an appliance manufacturer claims to have developed a compact microwave oven that consumes a mean of no more than 250 W with a population standard deviation of 15 W.
They take a sample of 20 microwave ovens and find that they consume a mean of 257.3 W.
Let = <u><em>mean power consumption for microwave ovens.</em></u>
So, Null Hypothesis, :
250 W {means that a compact microwave oven consumes a mean of no more than 250 W}
Alternate Hypothesis, :
> 250 W {means that a compact microwave oven consumes a mean of more than 250 W}
The test statistics that would be used here <u>One-sample z test statistics</u> as we know about the population standard deviation;
T.S. = ~ N(0,1)
where, = sample mean power consumption for ovens = 257.3 W
σ = population standard deviation = 15 W
n = sample of microwave ovens = 20
So, <em><u>the test statistics</u></em> =
= 2.176
The value of z test statistics is 2.176.
<u>Now, at 0.05 significance level the z table gives critical value of 1.645 for right-tailed test.</u>
Since our test statistic is more than the critical value of t as 2.176 > 1.645, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which <u>we reject our null hypothesis</u>.
Therefore, we conclude that a compact microwave oven consumes a mean of more than 250 W.
✪ Both triangles will be proven similar by AA theorem i.e. Angle-Angle theorem.
✪ The symbol for similarity is ~.
✪ The symbol for congruency is ≅.
